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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) Arakelov theory; Néron pairing; potential theory; Green's pairings; non-archimedean local fields; intersection theory Harbater, D.: Potential theory over local and global fields, II. J. algebra 148, 384-432 (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) covers of the line; local-global questions; \(p\)-adic fields; \(G\)-cover; inverse Galois problem; Galois group; field of moduli; field of definition Dèbes, P.: G-covers ofp1. Contemp. math. 186, 217-238 (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) Borel-Moore homology; blowup equation; Hirota differential; Hilbert scheme of points; equivariant \(K\)-Theory; localisation theorem; Grothendieck group; Uhlenbeck compactification; Whitham hierarchy; Hilbert series; super-symmetric Yang-Mills theory; Young diagram Nakajima, Hiraku; Yoshioka, Kōta, Instanton counting on blowup. I. 4-dimensional pure gauge theory, Invent. Math., 162, 2, 313-355, (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) minimal models of families of threefolds; Mori theory; deformation families; terminal singularities; flips for families; small contractions; Reid's conjecture J. Kollár and S. Mori, Classification of three-dimensional flips, J. Amer. Math. Soc. 5 (1992), no. 3, 533-703. | 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) good postulation; specialization; degeneration; double line; double point; generic union of lines; sundial; residual scheme; Hartshorne-Hirschowitz theorem; Castelnuovo's inequality; Hilbert 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) flat line bundles; Ueda's theory; blow-up of the three-dimensional projective space at eight points Koike, T, Toward a higher codimensional ueda theory, Math. Z., 281, 967-991, (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) deterministic algorithm; \(p\)-adic modular counting of rational points; sparse polynomials over finite fields; Stickelberger theorem; Gross-Koblitz formula; Gauss sums Wan D.: Modular counting of rational points over finite fields. Found. Comput. Math. 8, 597--605 (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) primitive roots; Artin's conjecture; function field; Dirichlet density of prime ideals Clark, D. A.; Kuwata, M.: Generalized Artin's conjecture for primitive roots and cyclicity mod p of elliptic curves over function fields. Canad. math. Bull. 38, No. 2, 167-173 (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) Arithmetic theory of algebraic functions; Dedekind-Weber theory; algebraic function fields; linear systems; divisors; Abelian differentials | 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) Positive polynomials; sums of squares; quadratic modules; convex sets Lasserre J.B.: Representation of nonnegative convex polynomials. Arch. Math. 91(2), 126--130 (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 cycles; Chow ring; motives; Bloch-Beilinson filtration; hyperkähler variety; Lagrangian subvariety; constant cycle subvariety; (Hilbert scheme of) \(K3\) surface; Beauville's splitting property; multiplicative Chow-Künneth decomposition; spread of algebraic cycles | 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) class field theory for curves over local fields; abelian fundamental group; class field theory of two-dimensional local fields; reciprocity law Saito S.: Class field theory for curves over local fields. J. Number Theory 21(1), 44--80 (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) étale cohomology; real algebraic number fields; Artin-Verdier duality theorem Bienenfeld, M., An étale cohomology duality theorem for number fields with a real embedding., Trans. Amer. Math. Soc., 303, 1, 71-96, (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) Fontaine's ring; filtration; valuation of convergence; Artin conductor; Swan conductor; de Rham representation; filtration by ramification subgroups; \(p\)-adic representation P. Colmez, ''Fonctions d'une variable p-adique,'' Astérisque, 319, 187--212 (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) convex cone; decomposition of a positive polynomial; real algebraic geometry; moment problems; subnormal operators; sum of squares of polynomials M. Putinar, \textit{Positive polynomials on compact semi-algebraic sets}, Indiana Univ. Math. J., 42 (1993), pp. 969--984, . | 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) field of definition; Belyi's theorem; minimal surfaces; ruled surfaces; number 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) exponential sums; Igusa's conjecture; Igusa's local zeta functions; motivic oscillation index; non-rational singularities; analytic isomorphism of singularities | 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) identity between Faltings height of CM abelian variety and logarithmic derivative of Artin \(L\)-functions; elliptic modular form; arithmetic intersection; Siegel modular forms; Hilbert modular forms; Colmez conjecture Yang, T., \textit{the chowla-Selberg formula and the Colmez conjecture}, Canad. J. Math., 62, 456-472, (2010) | 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) Hecke characters of imaginary quadratic fields; weak Leopoldt's conjecture Bars, The weak Leopoldt's conjecture for Hecke characters of imaginary quadratic fields, J. Algebra 319 pp 1954-- (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) Hilbert's 17th problem; meromorphic function; Pfister's formula Francesca Acquistapace, Fabrizio Broglia, and José F. Fernando, On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 2, 333 -- 369. | 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) vector bundles on curves; coherent systems; moduli space of coherent systems; stable bundle; Brill-Noether theory of vector bundles; Butler's conjecture | 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) Lie algebroid; dg-Lie algebra; formal moduli problem; Koszul duality; deformation theory; derived infinitesimal thickening; Kodaira-Spencer; Schlessinger conditions; formal moduli problem; small extensions; \(\infty\)-category of Lie algebroids | 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 of algebraic function fields; realization of group as Galois group; Galois theory Henning Stichtenoth, Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper, Math. Z. 187 (1984), no. 2, 221 -- 225 (German). | 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) absolute Galois group of rational function field; real closed field; Tarski principle; transfer principle L P.D. v.d. Dries and P. Ribenboim , An application of Tarski's principle to absolute Galois groups of function fields , Queen's Mathematical Preprint No. 1984-8. | 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; positive polynomial; sum of squares; quadratic module; moment problem; optimization of polynomials J. Nie and M. Schweighofer, \textit{On the complexity of Putinar Positivstellensatz}, J. Complexity, 23 (2007), pp. 135--150. | 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) Arveson's resistant conjecture; graded Hilbert module; d-shift Hilbert module; essentially normal; stable division property; ring of polynomials O. M.SHALIT,\textit{Stable polynomial division and essential normality of graded Hilbert modules}, J. Lond. Math. Soc. (2) 83 (2011), no. 2, 273--289. http://dx.doi.org/10.1112/jlms/jdq054.MR2776637 | 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; algebraic fundamental group; plane curves; factorization of polynomials; resolution of plane curve singularities; hyperelliptic function fields; construction of Galois extensions; finite group; Galois group; PSL(2,8); unramified covering; affine line Shreeram S. Abhyankar, Square-root parametrization of plane curves, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 19 -- 84. | 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) generalization of class field theory; local fields; global fields; Milnor K-group; integral projective scheme; Chow group; generalization of ramification theory; higher dimensional schemes; generalized Swan conductor Kato, K. : A generalization of class field theory (Japanese) . Sûgaku 40 (1988) 289-311. | 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) semidefinite programming; spectrahedra; convex sets; sums of squares; linear matrix inequalities João Gouveia, Tim Netzer, Positive polynomials and projections of spectrahedra. arXiv:0911.2750, 2010. | 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) semisimplification; \(G\)-complete reducibility; geometric invariant theory; rationality; cocharacter-closed orbits; degeneration of \(G\)-orbits | 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 rings; Artin-Schelter regular algebras of global dimension three; noncommutative projective geometry; elliptic algebras; point modules; Noetherian domains; Hilbert series; elliptic curves -, Algebras associated to elliptic curves , Trans. Amer. Math. Soc. 349 (1997), 2317--2340. JSTOR: | 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) index theorem; analytic torsion; heat kernel of the Laplacian on Riemann manifolds; Arakelov's theory; hermitean bundles; Mordell conjecture; arithmetic intersection theory for general arithmetic varieties; arithmetic Riemann-Roch theory; arithmetic Chern classes; arithmetic \(K\)- groups; arithmetic Chow groups; Dirac operators on compact Kähler manifolds; super-Dirac operators [15] Faltings (G.).-- Lectures on the arithmetic Riemann-Roch theorem, Annals of Math. Studies, vol. 127, Princeton University Press, 1992. &MR~11 | &Zbl~0744. | 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 formula; conductor of algebraic Hecke characters; Gauss sums; relative Lubin-Tate groups; Hilbert symbol | 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) Gabriel filters; multiplicative filters; filters of finite type; real closed rings; complete ring of quotients N. Schwartz, Gabriel filters in real closed rings, Comment. Math. Helv. 72 (1997), 434--465. | 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) binary form; length; cabinet; sums of powers; Sylvester form; Hankel matrix; Hilbert identity B. Reznick, \textit{On the length of binary forms}, in Quadratic and Higher Degree Forms, Springer, New York, 2013, pp. 207--232. | 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) Calabi-Yau manifolds; strong fields; Hodge theory; nuclear algebraic surfaces; irreducible representation of SO(10); string 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) locally nilpotent derivations; additive group actions; Hilbert's fourteenth 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) symbolic powers; Waldschmidt constant; Chudnovsky's conjecture; containment problem; ideals of points; stable Harbourne conjecture | 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) Hitchin fibrations; non-abelian Hodge theory; algebraic surfaces; commuting schemes; Hilbert scheme of points | 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 curve; real divisor; Brill-Noether theory; Clifford's inequality Monnier, Very special divisors on real algebraic curves, Bull. Lond. Math. Soc. | 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) Abel's theorem; integrals of the second and third kind; metric theory 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) cell decomposition of modular varieties; Siegel modular group; Voronoi's reduction theory; analytic Whitney-stratification; Poincaré dual decomposition; Voronoi cells; Satake partial compactification MacPherson, R.; McConnell, M., Explicit reduction theory for Siegel modular threefolds, Invent. math., 111, 575-625, (1993) | 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) alternative algebra; quadratic algebra; composition algebras; algebraic curves of genus zero; locally ringed spaces; Cayley-Dickson doubling process; Zorn's vector matrices; octonion algebras; Zorn algebras; function fields of genus zero; polynomial rings Petersson, H.: Composition algebras over algebraic curves of genus 0. Trans. Am. Math. Soc. 337, 473--491 (1993) | 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) Mordell's conjecture over function fields; theorem of the kernel . Coleman, R.F. , '' Manin's proof of the Mordell conjecture over function fields '', preprint. | 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) Schottky problem; length of the shortest closed geodesic; Schottky locus; moduli space of principally polarized abelian varieties; period matrices which are not Jacobians; arithmetic lattice Peter Buser & Peter C. Sarnak, ``On the period matrix of a Riemann surface of large genus'', Invent. Math.117 (1994) no. 1, p. 27-56 | 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) topos; variable reals; separably real closed local ring; Dedekind reals; coherent axiomatization; semi-algebraic geometry; elimination of quantifiers DOI: 10.1016/0022-4049(86)90068-X | 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) triple contact of curves; Hilbert scheme; Schubert's enumerative calculus for triangles Roberts-Spelser , '' Enumerative Geometry of Triangles, III '' Comm. in Alg. 15(9) 1929-1966 (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) Castelnuovo-Mumford regularity; rational points in projective spaces over finite fields; Hilbert function; index of stability E. Kunz and R. Waldi, On the regularity of configurations of \(\mathbb{F}_q\)-rational points in projective space , J. Comm. Alg. 5 (2013), 269-280. | 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 scheme of a surface; vanishing theorem; Le Potier's strange duality conjecture; cohomology Danila, G, Sur la cohomologie d'un fibré tautologique sur le schéma de Hilbert d'une surface, J. Algebraic Geom., 10, 247-280, (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) function field analogue of the theory of elliptic modular curves; Drinfeld modules; Drinfeld's upper half-plane; expansions at the cusps of certain modular forms; Manin-Drinfeld theorem; algebraic modular forms; jacobian Ernst-Ulrich Gekeler, Drinfel\(^{\prime}\)d modular curves, Lecture Notes in Mathematics, vol. 1231, Springer-Verlag, Berlin, 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) rational functions; sums of squares; Pythagoras number; elliptic curve; Jacobian variety; divisor DOI: 10.1007/s00229-004-0535-0 | 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 representation; reductive group; geometry of flag manifold; fixed point theorem; Weyl's character formula; cohomology group; equivariant line bundle; real semisimple group; invariant eigendistribution; flag variety; Harish-Chandra modules; K-equivariant sheaves [K] Kashiwara, M.: Character, character cycle, fixed point theorem, and group representations. Adv. Stud. Pure Math.14, 369-378 (1988) | 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 mathematics; divisor theory; Krull domains; PvMD | 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) moduli problem; integrble systems; generic affine variety; flows of the integrable vector fields; geodesic flow Bueken, P. and Vanhaecke, P., The Moduli Problem for Integrable Systems: The Example of a Geodesic Flow on SO(4), J. London Math. Soc. (2), 2000, vol. 62, no. 2, pp. 357--369. | 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 scheme; compactification; Bott's formula; surface of degree \(d\) | 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) GIT; geometric invariant theory; degeneration; Hilbert scheme; expanded degenerations; Donaldson-Thomas invariants; Pandharipande-Thomas stable pairs; $K3$ surfaces; Hilbert scheme of points; Li-Wu stack; bipartite graph; smooth support; numerical support; GIT quotient; stack quotient; Deligne-Mumford stack | 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 subsets of codimension 1; semi-algebraic homeomorphism; real algebraic geometry; real spectrum; orders; valuation theory Coste, M.: Sous-ensemble algébriques réels de codimension 1. C. R. Acad. sci. 300, No. 1, 661-664 (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) algebraic variety; mod \(\ell \) algebraic K-theory; spectrum; Eilenberg- MacLane spectra; algebraic K-theory of fields; homotopy groups; Lichtenbaum-Quillen conjecture; complex K-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) Chevalley-Warning theorem; generic \(p\)-divisibility; \(L\)-function of exponential sums; zeros of polynomials over finite fields; Ax-Katz bound; weight of support set. | 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) invariant theory; Hilbert function of stratum | 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) Eightfold way; Klein's quartic curve; Riemann surfaces; algebraic curves; uniformization; modular curves; mathematics and art; visualization of mathematics; graphic art; JFM 11.0297.01 S. Levy, \textit{The eightfold way: the beauty of Klein}'\textit{s quartic curve}, Cambridge University Press, Cambridge U.K. (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) \(o\)-minimal; real closed fields; definable \(C^r\) groups; definable \(C^rG\) manifolds; definably compact | 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 equations; solvability problems; Abel's theorem; complex functions of one variable; Riemann surfaces; monodromy; differential Galois theory; regular polyhedra | 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) exponential height; diophantine equations; Bogomolov-Miyaoka-Yau inequality; arithmetic surface; Arakelov's intersection theory; intersection numbers; Szpiro conjecture; Parshin trick; asymptotic Fermat theorem; boundedness of the torsion of elliptic curves A. N. Parshin, ``The Bogomolov -- Miyaoka -- Yau inequality for the arithmetical surfaces and its applications'', Seḿinaire de theórie des nombres (Paris, 1986 -- 87), Progr. Math., 75, Birkhaüser, Boston, MA, 1988, 299 -- 312 | 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) Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. | 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) Prym map; Torelli problem for Prym varieties; double covering of a general curve; theta divisor; Petri's theorem Debarre, O., Sur le problème de Torelli pour LES variétés de Prym, Amer. J. Math., 111, 1, 111-134, (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) Diophantine systems; Rumely's local-global principle; constructions of varieties over global fields; prescribed local properties; constructions of Galois extensions of local fields with given groups --. --. --. --., ``Applications of local-global principles to arithmetic and geometry'' in Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry (Ghent, Belgium, 1999) , Contemp. Math. 270 , Amer. Math. Soc., Providence, 2000, 169--186. | 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) Mordell-Lang; Manin-Mumford; quantifier elimination; stability theory; differentially closed fields; separably closed 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) ring of polynomials; real algebraic variety; Hilbert space; Gaussian measure | 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 analytic theory of Teichmüller space; deformations; uniqueness; theorem; Fricke moduli; Teichmüller modular group; compactification; classification of; diffeomorphisms; fractional twist group; Fenchel- Nielsen; coordinates У. Абикоф, Вещественно аналитическая теория пространства Тейхмюллера, Математика. Новое в зарубежной науке, 38, Мир, М., 1985, 119 с. | 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) existence of coarse moduli space; weak positivity of dualizing sheaves; Hilbert polynomial; geometric invariant 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) deformation of complete intersection; Hilbert function; Artin algebras; peelable algebras Iarrobino, A.: Deforming complete intersection Artin algebras, appendix: Hilbert function of C[x,y]/I. Proc. sympos. Pure math. 40 (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) generalized Hamming weight; weight distribution; trace codes; fibre product of Artin-Schreier curves; rational points; supersingular curves van der Geer G., van der Vlugt M.: Fibre products of Artin--Schreier curves and generalized Hamming weights of codes. J. Combin. Theory Ser. A 70, 337--348 (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) diophantine equations; equations over finite fields; arithmetic theory of algebraic curves; nonstandard arithmetic; zeta function; integral points on curves S. A. Stepanov, \textit{Arithmetic of Algebraic Curves} (Nauka, Moscow, 1991) [in Russian]. | 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 number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. | 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) Dirichlet \(L\)-functions; moments of \(L\)-functions; function fields; finite fields; random matrix 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) meromorphic matrix functions; complex vector bundles; closed Riemann surface of arbitrary genus; first-order pole-zero meromorphic \(r\times r\) matrix function interpolation problem; linear homogeneous system of equations Ball, J. A. and Clancey, K.: Interpolation with meromorphic matrix functions, Proc. Amer. Math. Soc. 121 (1994), 491-496. | 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) number of rational points; finite field; Fermat curve; Waring's problem García, A.; Voloch, J.F., Fermat curves over finite fields, J. number theory, 30, 3, 345-356, (1988) | 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) Jacobi sums; Artin-Tate formula; submotives of the Fermat 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) solitons; dynamic equations of field theory; supersymmetries; coding 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) sums of squares; non-negative polynomials; Hankel matrices; Cayley-Bacharach; spectrahedra; apolar ideals | 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) étale cohomology; level; sum of squares; non-real function field of a rational surface Parimala, R.; Sujatha, R.: Levels of non-real function fields of real rational surfaces. Amer. J. Math. 113, 757-761 (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) theta-nullwerte; quantum gravity; Jacobians of compact Riemann surfaces; KP hierarchy; Riemann-Schottky problem; Liouville equation; string 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) elimination; solving systems of polynomial equations; mechanical theorem proving; decomposition of algebraic varieties; Hilbert's Nullstellensatz D.M. Wang, An elimination method based on Seidenberg's theory and its application, in:Computational Algebraic Geometry, Progress in Mathematics 109 (Birkhäuser, Boston, 1993) pp. 301-328. | 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 surface of general type; birational canonical map; Castelnuovo's second inequality; Castelnuovo's 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) conjugacy problem in Artin groups; classifications of surfaces; word problem in braid groups; conjugates of powers of generators; Artin groups of spherical type; algorithms | 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) analytic germs; analytic functions; sums of squares; Pythagoras number; positive extension property; coherent sheaves; Lojasiewicz inequality; Whitney umbrella Fernando, JF, On the positive extension property and hilbert's 17-th problem for real analytic sets, J. Reine Angew. Math., 618, 1-49, (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) positivstellensatz; sums of squares; nonnegativity; graph parameter; homomorphism density Netzer, Tim; Thom, Andreas: Positivstellensätze for quantum multigraphs. (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) real closed valued fields; separated analytic structure; overconvergent power series; \(o\)-minimality; weak \(o\)-minimality; \(C\)-minimality | 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) sums of squares; Pythagoras number; level; purity theorem in cohomology | 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 points; subvarieties; canonical height; nontrivial translates; torsion points; Lehmer's problem; points of minimal height E. Bombieri and U. Zannier, Algebraic points on subvarieties of \?\(^{n}\)_{\?}, Internat. Math. Res. Notices 7 (1995), 333 -- 347. | 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-Blumenthal abelian varieties; totally real fields Yu, C.-F.: On the supersingular locus in Hilbert-Blumenthal 4-folds. J. Algebraic Geom. 12, 653--698 (2003) | 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) sums of squares; complete intersection; unmixed surface germs; positive semi-definite function germ; mixed surface germs DOI: 10.1007/s00209-003-0519-x | 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) apolar theory; ideals of points; star configuration; Waring 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) differential modules; comparison theorems; integrable connections; regular singular connections; direct images; Gauss-Manin connections; Gauss maps; irregularity of connections; Turrittin exponents; Fuchs exponents; indicial polynomials; relative De Rham complex; fibrations; logarithmic differential operators; Riemann existence theorem; rigid-analytic cohomology; \(p\)-adic de Rham cohomology; Dwork's dual 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) elimination polynomials; resultants; Hilbert's 15th problem; Gröbner basis; Buchberger algorithm | 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) Gauss sum; Fourier transforms of relatively invariant functions; finite fields; Sato's fundamental theorem; prehomogeneous vector spaces Denef, J.; Gyoja, A.: Character sums associated to prehomogeneous vector spaces. Compositio math. 113, 273-346 (1998) | 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 surfaces; Abelian integrals; algebraic number theory; function fields; valuations; function fields of curves; Abel-Jacobi theorem Cohn, P. M.: Algebraic numbers and algebraic functions, Chapman \& Hall math. Ser. (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) elementary number theory; symmetric cryptosystems; DES-algorithm; secure block cipher; public key cryptosystems; prime number generation; primality tests; integer factorization; discrete logarithm; cryptographic hash functions; authentication codes; digital signature; Merkle's signature scheme; Lamport-Diffie-one-time signature scheme; finite fields and elliptic curves; identification; challenge-response-identification; zero-knowledge proofs; Shannon's theory; secret sharing; AES-algorithm; Rijndael cipher | 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) complex multiplication; \(K3\) surfaces; fields of definition; class field theory | 0 |
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