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Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Cartier-Dieudonné theory; sheaf of K-groups; augmented artinian local k-algebras; crystalline cohomology; formal Picard group; Artin-Mazur groups; Witt vector cohomology; Chow group Stienstra, J.: Cartier-Dieudonné theory for Chow groups. J. Reine Angew. Math. \textbf{355}, 1-66 (1985) (correction. J. Reine Angew. Math. \textbf{362}, 218-220 (1985)) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) unique factorization; congruence; quadratic reciprocity; quadratic Gauss sums; Jacobi sums; cubic and biquadratic reciprocity; equations over finite fields; zeta functions; quadratic and cyclotomic fields; Stickelberger relation; Eisenstein reciprocity law; Bernoulli numbers; Dirichlet L-functions; Mordell-Weil theorem for elliptic curves; Mordell conjecture; Taniyama-Weil conjecture; Fermat's last theorem; Birch- Swinnerton-Dyer conjecture; Gauss' class number conjecture K. Ireland and M. Rosen, \textit{A Classical Introduction to Modern Number Theory}, (2nd ed.), Springer, 1990. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Riemann's zeta-function; theory of residues | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real closed spaces; semi-algebraic spaces; open morphisms; dimension; number of connected components N. Schwartz, Open morphisms of real closed spaces, Rocky Mountain J. Math., to appear. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) degree of projective variety; Hilbert function; intersection theory; Bernstein-Kushnirenko theorem A. G. Khovanskii, ''Intersection theory and Hilbert function,'' Funct. Anal. Appl., vol. 45, pp. 305-315, 2011. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic function; enumerative problems; resolvent degree; Hilbert's 13th problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) differentially closed fields; finite rank definable sets; internality to the constants; Kolchin's differential tangent space | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) irreducible polynomials; prescribed coefficients; prescribed traces; Artin-Schreier curves; zeta functions; binary Kloosterman sums | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) overconvergent \(p\)-adic representation; Iwasawa theory of \(p\)-adic representations; \(p\)-adic representation; Fontaine's theory; generalized Hodge-Tate decomposition F. Cherbonnier and P. Colmez, Représentations p-adiques surconvergentes, Invent. Math. 133 (1998), no. 3, 581-611. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) non-archimedean valued fields; analytic functions; \(p\)-adic cohomology; Weil conjectures; \(p\)-adic analytic varieties; action of Frobenius; rigid cohomology; \(p\)-adic analytic functions; Morita's \(p\)-adic gamma function | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) tropical geometry; linear programming; mean payoff games; symbolic perturbation; Hahn series; real closed fields Allamigeon, X., Benchimol, P., Gaubert, S., Joswig, M.: Combinatorial simplex algorithms can solve mean payoff games. arXiv:1309.5925 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) cancellative monoids; presentations; combinatorial group theory; fundamental groups; complements of logarithmic free divisors; fundamental elements; generalizations of Artin groups; Artin monoids; growth functions K. Saito, T. Ishibe, Monoids in the fundamental groups of the complement of logarithmic free divisors in C\^{}\{3\}. J. Algebra 344, 137-160 (2011) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) inverse Galois theory; Noether's problem; rationality problem M. Kang, B. Plans, Reduction theorems for Noether's problem, Proc. Amer. Math. Soc. 137 (2009), 1867\ 1874. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's sixteenth problem; limit cycle; Abelian integral; Picard-Fuchs system; Hamiltonian systems \.Zolądek, H.: The monodromy group. Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) [Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series)], vol.~67, Birkhäuser Verlag, Basel (2006) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Weil bound; finite ground field; Artin-Schreier curves; number of points; polar curves Hefez, A.; Kakuta, N.: Polars of Artin--Schreier curves. Acta arith. 77, 57-70 (1996) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) crystalline cohomology; \(p\)-adic cohomology; \(p\)-adic discrete valuation rings; toroidal singularities; almost étale extensions; Frobenius mapping; Poincaré duality; Künneth formula; almost invariants; Artin-Schreier theory; isocrystals G. \textsc{Faltings}, Almost étale extensions, \textit{Astérisque}, \textbf{279} (2002), 185-270. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Clifford algebras; Euler characteristics; Quadratic fibrations; mirror symmetry; string theory; Calabi-Yau manifolds; nonlinear sigma models; Calabi-Yau manifolds; superstring theory; mirror symmetric pair; symplectic; Fukaya category; bounded derived category; Homological Projective Duality; complete intersection of quadrics; Lefshetz decomposition; non-commutative algebraic variety; Clifford non-commutative varieties; Hodge numbers; Batyrev's stringy Hodge numbers; Clifford-stringy Euler characteristics | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) determinant orbit closure; Latin squares; Alon-Tarsi conjecture; geometric complexity theory; Valiant's conjecture; representations Kumar, Shrawan, A study of the representations supported by the orbit closure of the determinant, Compos. Math., 151, 02, 292-312, (2015) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Dwork cohomology; rigid cohomology of a scheme of finite type; complete non-archimedean field; superconvergent crystal; Artin-Schreier-extension P. Berthelot , Cohomologie rigide et théorie de Dwork: le cas des sommes exponentielles , in Astérisque 119-120 (1984) 17-49. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) mixed Tate motives; special values of zeta and \(L\)-functions; totally real number fields Brown, F.: \textit{Dedekind zeta motives for totally real number fields}. Invent. Math. 194 (2013), no. 2, 257--311. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert functions of determinantal loci; bitableaux; determinantal polynomials; second fundamental theorem of invariant theory Shreeram S. Abhyankar, Determinantal loci and enumerative combinatorics of Young tableaux, Algebraic geometry and commutative algebra, Vol. I, Kinokuniya, Tokyo, 1988, pp. 1 -- 26. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) derivations; Hilbert fourteenth problem; additive group actions; invariants; finite generation of invariant ring Daigle, D.; Freudenburg, G., A note on triangular derivations of \(k [X_1, X_2, X_3, X_4]\), Proc. Am. Math. Soc., 129, 3, 657-662, (2001) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Harnack's inequality; real algebraic space curve; number of connected components; Castelnuovo's bound Pecker, D.: Un théoréme de Harnack dans l'espace. Bull. sci. Math. 118, 475-484 (1994) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) metabiosis; knowledge; acquisition; constructive theory of polynomial ideals Renschuch, B.; Roloff, H.; Rasputin, G. G.: Vergessene arbeit des leningrader mathematikers N.M. Gjunter zur theorie der polynomideale, Wiss. zeit. Pädagogische hochschule Potsdam 31, 111-126 (1987) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hasse-Weil zeta-functions; \(p\)-adic periods; \(p\)-adic fields; \(p\)-adic zeta functions; arithmetic of special values; zeta-functions; generalized Iwasawa main conjecture; Fontain's ring; explicit reciprocity laws; Lubin-Tate formal groups; dual exponential maps Kato, K.: Lectures on the approach to Iwasawa theory for Hasse-Weil \(L\)-functions via \(B_{\mathrm dR}\) II. Non publié | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's fourteenth problem; locally nilpotent derivations Den Essen, Arno Van: A simple solution of Hilbert's fourteenth problem in dimension five, Colloq. math. 105, No. 1, 167-170 (2006) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite fields; singular multiplicative character sums; cohomological interpretation of character sums; an upper bound for the sum of Betti numbers Rojas-León, A., Estimates for singular multiplicative character sums, Intern. Math. Res. Notices, 2005, 1221-1234, (2005) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) theta functions; rational characteristics; Jacobi's derivative formula; sum of two squares Matsuda, K, Analogues of jacobi's derivative formula, Ramanujan J., 39, 31-47, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) local fields; cohomology groups; ramification theory; infinite algebraic extensions; deeply ramified extensions; arithmetic of abelian varieties; infinite conductor; Kummer homomorphism; universal norm [12] J. Coates & R. Greenberg, `` Kummer theory for abelian varieties over local fields {'', \(Invent. Math.\)124 (1996), no. 1-3, p. 129-174. &MR 13 | &Zbl 0858.} | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) inverse problem of Galois theory; Galois covering of curves | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) abelian variety; theory ACFA; group definable in a model; model theoretic stability; 1-basedness; model companion of the theory of fields with an automorphism; Manin-Mumford conjecture; projective curve; Jacobian variety | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) standard basis; Gröbner basis; syzygies of a canonical curve; equations of Petri's type; non-minimal resolution; reducible canonical curves; Green's conjecture; second syzygy module; Hilbert's syzygy theorem Milnor, J.: On the 3-dimensional Brieskorn manifolds \textit{M(p, q, r)}. In: Neuwirth, L.P. (ed.) Knots, Groups, and 3-Manifolds (Papers Dedicated to the Memory of R. H. Fox), pp. 175-225. Princeton Univ. Press, Princeton, N. J. (1975) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(L\)-series of number fields; infinite-dimensional analogue of one- parameter group; Artin formalism; self-adjoint operator; associated heat kernel; characteristic kernel; trace; asymptotic expansion; regularized determinant of the Laplacian; Selberg zeta function; theta functions J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165-280. Zbl0789.11055 MR1263173 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) graded Artin algebra; Hilbert functions of sets of s points in \({bbfP}^ n\) Paolo Maroscia, Some problems and results on finite sets of points in \?\(^{n}\), Algebraic geometry --- open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin, 1983, pp. 290 -- 314. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Matsumoto-Montesino's theory; automorphisms of surfaces; monodromy; degeneration of curves; monodromies of degenerations; elliptic families | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Deligne-Mumford stack; algebraic stack; Hilbert stack; algebraic space; Artin stacks; quasi-projective schemes; moduli of families Vistoli, A.: The Hilbert stack and the theory of moduli of families. Geometry Seminars (Italian) (Bologna, 1988--1991), pp. 175--181. Univ. Stud. Bologna, Bologna (1991) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real closed fields; Bézout bound; semialgebraic varieties; connected components; incidence bounds Barone, S; Basu, S, On a real analog of Bezout inequality and the number of connected components of sign conditions, Proc. Lond. Math. Soc., 112, 115-145, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) elliptic curves over function fields; Tate-Shafarevich groups; explicit computation of \(L\)-functions; BSD conjecture; Gauss and Kloosterman sums | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) stratification of real semi-algebraic sets; decomposition; generalized point location problem B. Chazelle, H. Edelsbrunner, L. J. Guibas, and M. Sharir, A Singly-Exponential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications,Proc. 16th ICALP, Lecture Notes in Computer Science, Vol. 372, Springer-Verlag, Berlin, 1989, 179--193. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) elliptic curves; embedding degree; pairing-based cryptography; characters of fields; Jacobi sums DOI: 10.1016/j.cam.2010.08.020 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) irreducible algebraic curve; number field; algebraic torus of dimension at least 3; Levin; Zilber's Conjecture on Intersection with tori; transcendence theory; Shanuel's Conjecture; o-minimal structures Bays, M.; Habegger, P., A note on divisible points of curves, Trans. Amer. Math. Soc., 367, 1313-1328, (2015) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) coverings of singular curves; arithmetic genus; projective algebraic curves over a finite field; Weil conjectures; estimation of character sums over finite fields Aubry Y., Perret M.: A Weil theorem for singular curves, Proceedings of Arithmetic, Geometry and Coding Theory IV, ed. Pellikaan, Perret, Vląduţ. De Gruyter, (1995) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) translations of classics (algebraic geometry); history of algebraic geometry; mathematics of the 19th century; algebraic functions; function fields; algebraic curves; Riemann-Roch theorem; algebraic differential 2.R. Dedekind, H. Weber, \(Theory of algebraic functions of one variable.\) Translated from the 1882 German original and with an introduction, bibliography and index by John Stillwell. History of Mathematics, 39. American Mathematical Society (Providence, RI; London Mathematical Society, London, 2012), pp. viii+152 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) differential function field; algebraic differential equations; ADE; Galois theory; no movable singularity; Picard-Vessiot extension; Kolchin's theory; normal function fields; linearization property; complete integrable Hamiltonian systems; Euler equations Buium, A.: ''Differential function fields and moduli of algebraic varieties'', Lecture notes in math. 1226 (1986) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) equisingular deformation theory; moduli problem of plane curve singularities; Hamburger-Noether expansions; algebroid curve Campillo, A.: Hamburger-Noether expansions over rings. Trans. Am. Math. Soc. 279, 377-388 (1983) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's Nullstellensatz; ring-theoretic topics in advanced algebra; algebraic number theory; elementary algebraic geometry; arithmetic; prime ideals; integral domains; factorial rings; rational functions; formal power series; resultants Goblot, R.: Algèbre commutative, (1996) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Dif=Def problem; Smith-Thom inequality; maximal real surface; complex deformation class; surfaces of general type Kulikov, Vik.S., Kharlamov, V.M.: On real structures on rigid surfaces. Izv. Math. \textbf{66}(1), 133-150 (2002) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) self-dual codes; algebraic geometry codes; Gilbert-Varshamov bound; Tsfasman-Vladut-Zink bound; towers of function fields; asymptotically good codes; quadratic forms; Witt's theorem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) nonnegative real-analytic functions; sum of squares Jaworski P. (1982). Positive definite analytic functions and vector bundles. Bull. Acad. Polon. Sci. 30: 501--506 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Artin-Schreier curves; linear codes; dual of Melas code; Kloosterman curves; weights of geometric BCH codes; weights; survey; algebraic curves Lachaud, G.: Artin-Schreier curves, exponential sums, and coding theory. Theoret. comput. Sci. 94, 295-310 (1992) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Brauer group; period-index problem; real algebraic surfaces; u-invariant; Hodge theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) complexity; convexity; effective real algebraic geometry; linear matrix inequality; rational sum of squares; semidefinite programming Q. Guo, M. Safey El Din, and L. Zhi, \textit{Computing rational solutions of linear matrix inequalities}, in Proceedings of ISSAC, Boston, 2013. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sum of squares; positivstellensatz; nichtnegativstellensatz; moment problem Hà, HV; Ho, TM, Positive polynomials on nondegenerate basic semi-algebraic sets, Adv. Geom., 16, 497-510, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) enumerative geometry; computations in K-Theory; Donaldson-Thomas theory; moduli spaces; Hilbert schemes of points in threefolds; Nakajima varieties; stable envelops and quantum groups; quantum Knizhnik-Zamolodchikov equations A. Okounkov, \textit{Lectures on K-theoretic computations in enumerative geometry}, arXiv:1512.07363 [INSPIRE]. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sum of squares; positivstellensatz; polynomial optimization; Scheiderer's local-global principle; Morse function; non-degenerate polynomial map C.-T. Le, Nonnegative Morse polynomial functions and polynomial optimization, Positivity 20 (2016), no. 2, 483--498. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Kodaira-Spencer maps; transform of Hilbert functions; tangentially flat morphisms; deformations; Artin-Rees filtrations Herzog M., J. Algebra 120 pp 383-- | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) arithmetic field; class field theory; Galois group of the maximal Abelian extension; Abelianised fundamental group of an arithmetic scheme; fields of higher dimension; Milnor K-theory; non-Archimedean local field; norm map | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) greatest common divisor; sums of squares; semidefinite programming; global minimization Li, B.; Nie, J.; Zhi, L.: Approximate gcds of polynomials and sparse Sós relaxations, Theoret. comput. Sci. 409, No. 2, 200-210 (2008) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic curves; algebraic function fields; positive characteristic; automorphism groups; Artin-Schreier-Mumford curve Korchmáros, G.; Montanucci, M., The geometry of the Artin-Schreier-Mumford curves over an algebraically closed field, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) hyperbolic complex manifold; hyperbolicity problem; complex projective space; McQuillan's techniques for hyperbolicity of surfaces; techniques of Bloch for the setting of abelian varieties; techniques of Clemens-Ein-Voisin Y.-T. Siu, ''Hyperbolicity in complex geometry,'' in: The Legacy of Niels Henrik Abel, Springer-Verlag, Berlin, 2004, 543--566. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Ordered fields; Real algebraic geometry; Proceedings; Meeting; San Francisco Dubois, D. W.: Ordered fields and real algebraic geometry. AMS contemporary mathematics 8 (1982) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) nonconvex optimization; positive polynomial; sum of squares; moment problem; Positivstellensatz; semidefinite programming M. Schweighofer, \textit{Optimization of polynomials on compact semialgebraic sets}, SIAM J. Optim., 15 (2005), pp. 805--825. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) discriminant; pairing on curves; intersection number of horizontal divisors; Green's functions; divisor group; arithmetic surface; Arakelov theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) action of linear algebraic group; unramified Brauer group; rationality problem; fields of invariants Saltman, D. J.: Multiplicative field invariants and the Brauer group. J. algebra 133, 533-544 (1990) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) representation theory of finite-dimensional algebras; tame hereditary algebras; tame bimodules; noncommutative curves of genus zero; noncommutative function fields of genus zero D. Kussin, Parameter curves for the regular representations of tame bimodules, J. Algebra, 320 (2008), no. 6, 2567--2582.Zbl 1197.16017 MR 2437515 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Galois representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (1989). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Positivstellensatz; complexity; positive polynomial; sum of squares; preordering; moment problem; optimization of polynomials Schweighofer, M, On the complexity of schmüdgen's positivstellensatz, J. Complex., 20, 529-543, (2004) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) automorphism groups; cancellation problem for function fields; function fields of general type; Zariski problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) characteristic \(p\); \(p\)-closed rational vector fields; \(K3\) surfaces; unirational surfaces; Hirzebruch surfaces; Zariski surfaces; Enriques' surfaces; surfaces of general type; Artin invariant; quasi-elliptic surfaces M. Hirokado, Zariski surfaces as quotients of Hirzebruch surfaces by \(1\)-foliations , Yokohama Math. J., 47 (2000), 103--120. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) non-complete linear system of hyperplane sections; Green's theory; abelian variety Birkenhake C. (1996). Noncomplete linear systems on abelian varieties. Trans. Am. Math. Soc. 348(5): 1885--1908 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 16th problem; Casson-Gordon invariants; graph manifold; graph link | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) constructive resolution of the singularities; Hilbert-Samuel function Villamayor, Orlando, Constructiveness of Hironaka's resolution, Ann. Sci. École Norm. Sup. (4), 22, 1, 1-32, (1989) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) evaluation code; ordered domain; valuation; families of error correcting codes; decodified by the Berlekamp-Massey-Sakata algorithm; bounds for their minimum distance Galindo, C; Sanchis, M, Evaluation codes and plane valuations, Des. Codes Crypt., 41, 199-219, (2006) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) abelian integral; limit cycle; Hilbert's 16th problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real Picard-Vessiot theory; linear algebraic groups; group cohomology; real forms of algebraic groups | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) variation of mixed Hodge structure; mixed Hodge structure on Sullivan's 1-minimal model; flat bundle; Hodge theory; Kähler manifold | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic K-theory; norm residue homomorphism; \(K_ 2\) of fields; Brauer group; Merkur'ev-Suslin theorem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) torus action; Morse homology; Hilbert scheme of points; motivic homotopy theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) realization of motif of modular form by abelian variety; Hilbert; modular cusp form; totally real number field; Hilbert modular variety; Hecke algebra; Eichler-Shimizu correspondence T. Oda : Hodge structures of Shimura varieties attached to the unit groups of quaternion algebras , in Advanced Studies in Pare Mathematics 2: Galois Groups and Their Representations , 15-36 Tokyo: Kinokuniya Press (1983). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Boolean locales; orthogonal category; manuals of operations; quantum mechanics; sheaves of Hilbert spaces; empirical set theory; category of sheaves of sheaves of abelian groups Nishimura, H. (1995b). Empirical algebraic geometry,International Journal of Theoretical Physics, to appear. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite fields; maximal curves; genus; Hasse-Witt invariant; Cartier operator; Fermat curves; Artin-Schreier curves; hyperelliptic curves Garcia, Certain maximal curves and Cartier operators, Acta Arith. 135 pp 199-- (2008) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) monodromy functor; logarithmic connections; multiplicative preprojective algebras; vector bundles on punctured Riemann surfaces; Hilbert's 21st problem Crawley-Boevey (W.).-- Monodromy for systems of vector bundles and multiplicative preprojective algebras. Bull. London Math. Soc. 45, p. 309-317 (2013). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) evaluation codes; parametrized codes; parameters of a code; index of regularity; Hilbert function; minimum distance | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Artin-Schreier curve; moduli space of hyperelliptic curves; p-rank R. Pries, The \(p\)-rank stratification of Artin-Schreier curves, Ann. l'Institut Fourier, 62, 707, (2012) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) differential graded categories; Drinfeld's DG quotient; Morita equivalence; noncommutaive Chow motives; noncommutative mixed motives; noncommutative motivic Galois group; noncommutative pure motives; witt vectors; Morel-Voevodsky's motivic homotopy theory; noncommutative mixed Artin motives; Kimura finiteness; Grothendieck derivators Tabuada, Gonçalo, Noncommutative motives, with a preface by Yuri I. Manin, University Lecture Series 63, x+114 pp., (2015), American Mathematical Society, Providence, RI | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) geometric transitions; conifold transitions; mirror symmetry; Reid's fantasy; vacuum degeneracy problem; reverse transition; toric degenerations; moduli spaces of Calabi-Yau three-folds Rossi, M.: Geometric transitions. J. Geom. Phys. \textbf{56}, 1940 (2006). arXiv:math/0412514 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Artin's braid group; representation as subgroup of the symplectic group of \(2g\) by \(2g\) matrices with integral element W. Magnus and A. Peluso, On a theorem of V. I. Arnol'd, Comm. Pure Appl. Math. 22 (1969), 683-692. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic geometry; positive polynomials; sum of squares; semidefinite programming Lasserre J.B. (2005). SOS approximations of polynomials nonnegative on a real algebraic set. SIAM J. Optim. 16: 610--208 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert schemes; orbifold Euler characteristics; irreducible components of exceptional set; superstring theory; McKay correspondence Ito, Y., Nakamura, I.: McKay correspondence and Hilbert schemes. Proc. Japan Acad. Ser. A Math. Sci., 72, 135--138 (1996) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) twin irreducible polynomials; parity barrier over function fields; short character sums; level of distribution for irreducible polynomials | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) prehomogeneous vector space; adelization; \(p\)-adic field; \(v\)-adic completion; Sato-Shintani's theory; residues of zeta functions; Shintani zeta function Yukie, A., Shintani zeta functions, London Math. Soc. Lecture Note Ser., vol. 183, (1993), Cambridge University Press Cambridge | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) inverse Galois theory; Galois coverings; rigid analytic spaces; Galois extensions of function fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) rational curve; formally real field; space of orderings; dense orbits property; \(Q_ 1\)-fields; function fields of real algebraic varieties; elliptic curve | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hardy-Littlewood method; exponential sums; Waring's problem; equations in many variables; rational points; representation problems | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) infinite dimensional Hilbert manifolds; compact simple Lie group; smooth based loops; Kač-Moody groups; flag manifold; homogeneous Kähler metrics; curvature; representation theory; intrinsic geometry; first Chern class; dual Coxeter number; Fredholm structure; holonomy bundle; index theorem; families of Fredholm operators; affine Kač-Moody group; Kač character formula; instantons on the 4-sphere Freed, D.: Flag manifolds and infinite dimensional Kähler geometry. Infinite dimensional groups (1985) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) effectivity; effective version of Hilbert's Nullstellensatz; elimination P. Philippon , A propos du texte de W.D. Brownawell: ''Bounds for the degrees in the Nullstellensatz'' , Annals of Math 127 ( 1988 ), 367 - 371 . MR 932302 | Zbl 0641.14002 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) computations in algebraic geometry; ideal membership problem; solving polynomial equations; elimination theory; robotics; automatic geometry theorem proving; computations in commutative algebra; Gröbner base; Buchberger's algorithm D. Cox, J. Little, and D. O'Shea, \textit{Ideals, Varieties, and Algorithms: An introduction to Computational Algebraic Geometry and Commutative Algebra} (Springer-Verlag, New York, 1992; Mir, Moscow, 2000). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) quantifier elimination; real closed fields; Thom encoding; sign determination | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) constructivism; Galois theory; factorization of polynomials; splitting field; binary quadratic forms; composition of forms; Newton's polygon; genus; theorem of Riemann-Roch; Sylow's theorems | 0 |
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