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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) Chow ring; enumerative geometry; Hilbert scheme of points; intersection 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) lattice; maximal mediated set; nonnegativity; sum of nonnegative circuit polynomials; sums of squares
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) fields of real algebraic functions; reduced Whitehead group; Hasse principle; norm mapping
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) sheaf of regular functions; first cohomology group; algebraically 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) rational points; affine varieties; finite fields; complete intersection; exponential sums; asymptotic formula; upper estimate; number of integral points \beginbarticle \bauthor\binitsW. \bsnmLuo, \batitleRational points on complete intersections over \(\F_p\), \bjtitleInt. Math. Res. Not. IMRN \bvolume1999 (\byear1999), page 901-\blpage907. \endbarticle \OrigBibText W. Luo, Rational points on complete intersections over \(\F_p\), Inter. Math. Res. Notices , 1999 (1999), 901-907. \endOrigBibText \bptokstructpyb \endbibitem
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) polarized \(K3\) surfaces; Tate's conjecture for \(K3\) surfaces; finitely generated fields of odd characteristic; Kuga-Satake abelian varieties Madapusi Pera, K., \textit{the Tate conjecture for K3 surfaces in odd characteristic}, Invent. Math., 201, 625-668, (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) elimination; greatest common divisor of polynomials; Hermite's method; real algebraic geometry; computer aided geometric design Gonzalez-Vega, L.; Gonzalez-Campos, N.: Simultaneous elimination by using several tools from real algebraic geometry. J. symb. Comput. 28, 89-103 (1999)
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; Shafarevich's conjecture; free profinite group; quasi-free profinite group; function field; real closed field; Laurent series field Harbater, D., On function fields with free absolute Galois groups, Journal für die Reine und Angewandte Mathematik, 632, 85-103, (2009)
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) modular invariant theory; algebra of invariants; module of covariants; Hilbert series
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) effective computation of Hilbert's zero theorem; complexity Krick, T.; Pardo, L. M.: Une approche informatique pour l'approximation diophantienne. C. R. Acad. sci. Paris sér. I 318, 407-412 (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) Artin conductor; efficient conductor; curves over local fields; sheaf of differential modules
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) Namba's conjecture; hypergeometric series over finite fields; elliptic curves; trace of the Frobenius map Koike, M., Orthogonal matrices obtained from hypergeometric series over finite fields and elliptic curves over finite fields, Hiroshima Math. J., 25, 1, 43-52, (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) Hilbert scheme of points on a surface; obstruction theory; generating series of virtual Euler characteristics; tautological sheaf
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) moment relaxation; Lasserre relaxation; basic closed semialgebraic set; sum of squares; polynomial optimization; semidefinite programming; linear matrix inequality; spectrahedron; semidefinitely representable 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) unipotent group action; Hilbert's fourteenth problem Ryuji Tanimoto, Linear counterexamples to the fourteenth problem of Hilbert, J. Algebra 275 (2004), no. 1, 331 -- 338.
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 moduli; Field of definition; Fibered product; Going-up theorem; Hilbert's Nullstellensatz
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) parallel algebraic complexity; NC complexity; real algebraic numbers; Thom's lemma; multivariate Sturm theory Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M. F.: NC algorithms for real algebraic numbers, applicable algebra in engineering. Comm. comput. 3, 79-98 (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) automorphism of curves; families of curves; Artin-Schreier covers; special groups; additive polynomials Rocher, M., Large \(p\)-group actions with a \(p\)-elementary abelian derived group, J. Algebra, 321, 2, 704-740, (2009)
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 subgroups of rotation group; groups; linear algebra; infinite dimensional spaces; systems of linear differential equations; symmetry; free groups; generators; relations; Todd-Coxeter algorithm; bilinear forms; spectral theorems; linear groups; group representations; rings; algebraic geometry; factorization; modules; function fields and their relations to Riemann surfaces; Galois theory Artin, M.: Algebra. Prentice-Hall, Englewood Cliffs (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) connectedness of the real locus; Hilbert scheme
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) eta invariants; signature defects of cusps; special values of L- functions; cusp on Hilbert modular variety; lattice in totally real field; Hirzebruch L-polynomial; Hirzebruch signature theorem; flat connection; Feynman-Kac representation of the heat kernel Atiyah, MF; Donnelly, H; Singer, IM, Eta invariants, signature defects of cusps, and values of \(L\)-functions, Ann. Math., 118, 131-177, (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) string theory; space of moduli of closed Riemann surfaces Harris, R. (1987).The language machine. London: Duckworth.
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) strict simple degenerations; geometric Invariant theory; Hilbert schemes; good minimal dlt models; type II degenerations of \(K3\) surfaces
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 surface; Arakelov theory; discriminant; pairing on curves; intersection number of horizontal divisors; Green's functions; divisor group Harbater, D.: Arithmetic discriminants and horizontal intersections. Mathematische annalen 291, 705-724 (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) arithmetical ring; Bézout ring; coherent ring; constructive; Hilbert's program; local-global; \(pp\)-ring; projective module; Prüfer ring; Quillen-Suslin; rereading principle Lombardi, H.; Quitté, C.; Yengui, I., Hidden constructions in abstract algebra (6) the theorem of maroscia, brewer and costa, J. pure appl. algebra, 212, 1575-1582, (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) Heisenberg group; deformation theory; stack; hyperelliptic curves; moduli of vector bundles; heat equations; heat operators; Hitchin's connection DOI: 10.1090/S0894-0347-98-00252-5
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 points on Fermat curves over finite fields; intersection multiplicity; Bézout's theorem; Frobenius degeneration; intersection multiplicities Hefez, A.; Kakuta, N.: New bounds for Fermat curves over finite fields. Contemp. math. 123, 89-97 (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) Donaldson-Thomas theory of DM stacks; quantum cohomology; 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) finite-dimensional vector space; irreducible representations; unitary group; holomorphic line bundle; flags; Hilbert space; manifold of flags; quantum field theory; integrable systems A. G. Helminck and G. F. Helminck, \(H_k\)-fixed distributionvectors for representations related to \(\mathfrak p\)-adic symmetric varieties, 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) number of mappings of algebraic curves; theorem of De Franchis; Mordell's conjecture over functions 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) theta-functions; basic hypergeometric series; q-continued fractions; Rogers-Ramanujan continued fraction; Rogers-Ramanujan identities; basic theory of elliptic functions; Ramanujan's Eisenstein series; Jacobian elliptic functions; modular equations; theta-function identities B. C. Berndt, \textit{Ramanujan's Notebooks, Pt. III}, Springer, New York (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) non-negative univariate polynomials; Nichtnegativstellensätze; sum of squares decomposition; root isolation; real algebraic geometry
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) unramified class theory; reciprocity map; surfaces over local fields; Milnor \(K\)-groups; Chow groups; semistable reduction; deformation of degenerate hypersurfaces Sato K. (2005). Non-divisible cycles on surfaces over local fields. J. Number Theory 114(2): 272--297
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) Gram spectrahedra; extreme points; Pataki inequalities; binary forms; sums of squares
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) nonalgebraically closed ground field; real divisor class group; factorial coordinate domain; ideal of definition Margherita Roggero, Sui sistemi lineari e il gruppo delle classi di divisori di una varietà reale, Ann. Mat. Pura Appl. (4) 135 (1983), 349 -- 362 (1984) (Italian).
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 of points; \(r\)-fold symmetric product of projective surface; deformation theory Fantechi, B., Deformation of Hilbert schemes of points on a surface, Compos. Math., 98, 2, 205-217, (1995), MR 1354269
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 square representation; projective Positivstellensatz; totally real divisor Scheiderer, C., A positivstellensatz for projective real varieties, \textit{Manuscripta Mathematica},, \textit{138}, 1, 73-88, (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) Hilbert modular forms; totally real fields; Galois representations
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 spaces of sheaves; Vafa-Witten theory; Donaldson theory; 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) effective lower bounds; linear forms in logarithms of algebraic numbers; analytic subgroup theorem; algebraic groups; isogenies of abelian varieties; Tate's conjecture; semisimplicity of the Tate module; 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) hyperbolic polynomial; hyperbolicity cone; sums of squares; Bézoutian
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; invariants of vectors; invariants of matrices; polarization; restitution; Capelli's theorem Kraft, H.: Klassische Invariantentheorie. Eine Einführung, Algebraische Transformationsgruppen und Invariantentheorie, DMV Sem., vol. 13, , pp. 41-62. Birkhäuser, Basel (1989) (German)
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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) classification up to isomorphism; elementary equivalence; function fields over algebraically closed fields; function fields of curves; elliptic curves D. Pierce , Function fields and elementary equivalence . Bull. London Math. Soc. 31 ( 1999 ), 431 - 440 . MR 1687564 | Zbl 0959.03022
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) norm pairing; Galois representations; formal group of finite height; Hilbert's symbol; local field; Tate module; isogeny Benois, D. G.; Vostokov, S. V., Norm pairing in formal groups and Galois representations, Leningr.Math. J., 2, 1221-1249, (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) Finite fields; additive and multiplicative characters; mixed character sums; sheaves theory; Fourier transform; Lefschetz trace formula; cohomology groups; Euler-Poincaré formula
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) Newton polygons of curves; Artin-Schreier curves; Torelli locus
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 powers of linear forms; Waring's problem for algebraic forms Chipalkatti, J.: The Waring loci of ternary quartics. Exp. math. 13, No. 1, 93-101 (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) finite fields; maximal curves; genus spectrum; classification problem; towers of curves Garcia A.: On curves with many rational points over finite fields. In: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, pp. 152--163. Springer, Berlin (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) algebraic group; ring of polynomial invariants; constructive invariant theory; minimal generating set; torus
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) global generalization of Honda's result; formal groups; Gauss sums; integral representations; characters of odd prime conductor Childress, N.; Stopple, J.: Formal groups and Dirichlet L-functions, II. J. number theory 41, 295-302 (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) 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) non-negative polynomials; sums of squares; symmetric polynomials; symmetric inequalities; symmetric group
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) zero estimates; Cayley-Chow forms; effective elimination; algebraic independence; local generalization of Liouville's inequality; Hilbert Nullstellensatz Brownawell ( W.D. ) .- Applications of Cayley-Chow forms , dans '' Journées arithmétiques, ULM 1987 '', Lecture notes , Springer 1380 ( 1989 ), pp. 1 - 18 . MR 1009790 | Zbl 0674.10031
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 invariant theory; Diophantine approximation; Roth's theorem; Berkovich spaces; height of semi-stable 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) Newton's method; certified solutions; alpha theory; real solutions; numerical algebraic geometry
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) level of affine algebra; sum of squares; real point; semi-algebraic set; positiv-stellensatz; Positivstellensatz Mahé, L.: Sommes de carrés et anneaux de Witt réduits. C. R. Acad. sci. 300, 5-7 (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) polynomial endomorphism; zeros of a polynomial map; real-closed field; quadratic form
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) polynomial optimization; sum of squares; semidefinite programming; moment problem; Hankel matrix; flat extension; GNS construction; noncommutative polynomial; trace
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 real algebraic group; linearization problem; injectivity of complexification 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) quadratic forms; intersection; sums of two squares; circle method; asymptotic; Kloosterman refinement
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 fields; finite fields; hyperelliptic curves; lower bounds for moments; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory Andrade, J. C.: Rudnick and soundararajan's theorem for function fields. Finite fields appl. 37, 311-327 (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) multiplicative structure; skew fields over number fields; Hasse; norm principle; algebraic group; group of rational points; quadratic forms; Skolem-Noether theorem; algebra of quaternions; class field theory; direct subgroup; Spin(f); SL(1,D); trace Platonov V P and Rapinchuk A S, Proceedings of Steklov Institute of Math. 1985, Issue 3
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) computational number theory; elliptic curve method; probabilistic algorithm; factorization method; multiplicative groups of elliptic curves over finite fields; running time; comparison Lenstra, H. W., Factoring integers with elliptic curves, \textit{Annals of Mathematics}, 126, 3, 649-673, (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 bound; number of points; extension fields; exponential sums; function fields over finite 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) Mumford curves; Artin-Schreier-Mumford curves; automorphisms of curves G. Cornelissen and F. Kato, Mumford curves with maximal automorphism group, Proceedings of the American Mathematical Society 132 (2004), 1937--1941.
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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) 17-th Hilbert problem. Bibliography; real algebraic geometry
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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) ramification of surface; Artin-Schreier extension; Young diagram M. Oi, On ramifications of Artin-Schreier extensions of surfaces over algebraically closed fields of positive characteristic II, in preparation.
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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) rationality questions; rational points; Hasse-Weil \(L\)-function of modular elliptic curves; local-global principles; Selmer's curve; smooth projective varieties; Tate-Shafarevich group; Tate-Shafarevich conjecture; Selmer groups of elliptic curves; class field theory; Kolyvagin test classes Mazur B.: On the passage from local to global in number theory. Bull. Amer. Math. Soc. (N.S.) 29(1), 14--50 (1993)
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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) dynamical system; Darboux integrability; Hilbert's 16th problem; Liouville integrability Zhang X, \textit{Integrability of Dynamical Systems: Algebra and Analysis}, Springer, Singapore, 2017.
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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) real prime divisors; real closed subfield; semi-algebraic subset of the regular real points; Nash arcs; Nash wing selection lemma; real spectrum Robson R., Nash wings and real prime divisors
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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) real quadratic function fields; Ankeny-Artin-Chowla theorem; function fields; fundamental unit Yu, J.; Yu, J. -K.: A note on a geometric analogue of ankeny--Artin--chowla's conjecture. (1998)
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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) defects of cusp singularities; totally real cubic number field; plurigenera of Hilbert modular varieties; non-rational Hilbert modular threefold; arithmetic genus Grundman, H.G.: Defects of cusp singularities and the classification of Hilbert modular threefolds. Math. Ann.292, 1-12 (1992)
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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) convex algebraic geometry; sums of squares; Pythagoras number; linear syzygies
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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) curves over arithmetic ground fields; fundamental groups; categories; localization of categories; graph theory; profinite groups; free nonabelian groups Mochizuki S., Semi-graphs of anabelioids, Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, 221-322.
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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) compactification of moduli space of stable rank 2 vector bundles; space of reguli; Hilbert scheme; Grassmannian; geometric invariant theory; Poncelet quadric bundle
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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) elongated hypocycloid; handkerchief singularity; Whitney umbrella; sphere inversion; real sextic surface; models of the real projective plane \(\mathbb RP^ 2\) in Euclidean 3-space; Steiner surface; Veronese surface; crosscap; Rheinhardt's heptahedron; immersions; explicit Boy surfaces Apéry, F., \textit{Models of the Real Projective Plane: Computer Graphics of Steiner and Boy Surfaces}, Braunschweig: Vieweg, 1987.
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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) Thue-Siegel theorem; Faltings theorem; generalisation of Roth's theorem and Mordell's conjecture; Arakelov theory; arithmetic divisors; arithmetic discriminant; height; effective divisor Vojta, P., \textit{A generalization of theorems of faltings and thue-Siegel-Roth-wirsing}, J. Amer. Math. Soc., 5, 763-804, (1992)
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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) fans; real spectra of noncommutative rings; real places; orderings; order compatible real places; integral domains; Bröcker's trivialization theorem; quantum planes Marshall, M., Zhang, Y.: Orderings, real places and valuations on noncommutative integral domains. J. Algebra 212, 190--207 (1999)
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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) class field theory of arithmetical schemes; Bloch's exact sequence; reciprocity theorem; abelian fundamental group; idele class groups S. Saito, Unramified class field theory of arithmetic schemes, Ann. Math., 121 (1985), 251--281.
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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) positive characteristic; invariants of coverings; Artin-Schreier coverings of simple type; ample branch loci Takeda, Y, \textit{Artin-Schreier coverings of algebraic surfaces}, J. Math. Soc. Japan, 41, 415-435, (1989)
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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) real spectrum; quantifier elimination; applications of model theory; real algebraic geometry M. A. Dickmann, Applications of model theory to real algebraic geometry. A survey, Methods in mathematical logic (Caracas, 1983) Lecture Notes in Math., vol. 1130, Springer, Berlin, 1985, pp. 76-150.
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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) group schemes; torsors; Kummer Theory; Artin-Schreier Witt Theory
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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) Calabi-Yau manifolds; moduli spaces of Kähler manifolds; Hilbert schemes; toric varieties; \(D\)-branes; quantum field theory Mohri, K.: Kähler moduli space for a D-brane at orbifold singularities
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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) projective modules, Quillen-Suslin's theorem, arithmetical rings, constructive mathematics S. Barhoumi, H. Lombardi, I. Yengui, Projective modules over polynomial rings: A constructive approach, preprint, 2006
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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) algebraic curves; Hasse-Weil's bound; character sums; Fermat curves; finite fields
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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) real-pseudoconvex domains; analogs of Poincaré's Lemma
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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) Hilbert scheme of smooth connected curves; Brill-Noether theory; double covers
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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) symmetric tensor; sums of powers of linear polynomials; Waring problem; Waring rank; open Waring rank Jelisiejew, J.; An upper bound for the Waring rank of a form; Arch. Math.: 2014; Volume 102 ,329-336.
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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) eta invariants; signature defects of cusps; special values of; L- functions; cusp on Hilbert modular variety; lattice in totally; real field; Hirzebruch L-polynomial; Hirzebruch; signature theorem; flat connection; Feynman-Kac; representation of the heat kernel M. F. Atiyah, H. Donnelly, and I. M. Singer, Eta invariants, signature defects of cusps, and values of \?-functions, Ann. of Math. (2) 118 (1983), no. 1, 131 -- 177. , https://doi.org/10.2307/2006957 M. F. Atiyah, H. Donnelly, and I. M. Singer, Signature defects of cusps and values of \?-functions: the nonsplit case. Addendum to: ''Eta invariants, signature defects of cusps, and values of \?-functions'', Ann. of Math. (2) 119 (1984), no. 3, 635 -- 637.
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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) action of a finite group; orbifold Euler characteristic; string theory; Hilbert scheme of n points Hirzebruch F and Höfer T 1990 On the Euler number of an orbifold \textit{Math. Ann.} 286 255--60
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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) Noether's problem; rationality problem; Bogomolov multiplier; unramified Brauer groups; retract rationality; cohomology of finite groups Kang, M, Bogomolov multipliers and retract rationality for semi-direct products, J. Algebra, 397, 407-425, (2014)
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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) Cayley method; determinant; elimination theory; discriminants; resultants; Chow varieties; toric varieties; Newton polytopes; real algebraic geometry; hyperdeterminants; discriminant as the determinant of a Koszul complex I.M.~Gel'fand, M.M.~Kapranov and A.V.~Zelevinsky, \textit{Discriminants, resultants and multidimensional determinants}, Birkhäuser, Boston, 1994.
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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) Hilbert's fifteenth problem; Schubert calculus
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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) topological version of Weil's theorem; birational group law; group chunk; homogeneous group; quasi-algebraic group chunks; differentially algebraic group chunks; model theory; first-order definable L. P. D. van den Dries, Weil's group chunk theorem: a topological setting, Illinois J. Math. 34 (1990), no. 1, 127 -- 139.
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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) Carlitz module; Artin's conjecture; function fields
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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) deformation of a real surface; real closed field; perturbation; number of connected components of a hypersurface Coste M.: Épaississement d'une hypersurface algébrique réelle. Proc. Jpn. Acad. Ser. A. Math. Sci. 68(7), 175--180 (1992)
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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) characteristic numbers for plane cubics; nonsingular plane cubics; Hilbert's 15th problem; singular cubic curves Steven L. Kleiman and Robert Speiser, Enumerative geometry of nonsingular plane cubics, Algebraic geometry: Sundance 1988, Contemp. Math., vol. 116, Amer. Math. Soc., Providence, RI, 1991, pp. 85 -- 113.
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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) invariant sets; continuous dynamical systems; Ważewski's property; template; sum of squares
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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) actions of groups; linear algebra; topological groups; endomorphisms; Grassmannians; echelon matrices; groups preserving a bilinear form; quaternion fields; algebraic combinatorics; Lie groups; Platonic solids; topics from the projective plane; orthogonal groups; unitary groups; symplectic groups; Young tableaux; algebraic geometry; algebraic curves; surfaces configurations; special varieties; graphes; projective line; conics; representation theory; McKay correspondance Ph. Caldero, J. Germoni, \textit{Histoires Hédonistes de Groupes et de Géométries [Hedonistic Histories of Groups and Geometries].} Vol. 2, Calvage et Mounet, Paris, 2015.
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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) 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 André, Y., Baldassarri, F.: De Rham Cohomology of Differential Modules on Algebraic Varieties. Progress in Mathematics, vol.\ 189. Birkhäuser, Basel (2001)
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