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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) 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) survey articles (algebraic geometry); stacks; Artin stacks; moduli of vector bundles; curves over arithmetic ground fields; cohomology of algebraic stacks; Weil conjectures F. Neumann, Algebraic stacks and moduli of vector bundles, Publicações Matemáticas do IMPA , Colóquio Brasileiro de Matemática, 27, 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) fundamental group of a curve; Abhyankar conjecture; affine line; positive characteristic; Artin-Schreier covers Gille P. , Le groupe fondamental sauvage d'une courbe affine , in: Bost J.-B. , Loeser F. , Raynaud M. (Eds.), Courbe semi-stable et groupe fondamental en géométrie algébrique , Progress in Math. , 187 , Birkhäuser , 2000 , pp. 217 - 230 . MR 1768103 | Zbl 0978.14034 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) values at negative integers; p-adic Hilbert modular forms; abelian L-functions; totally real fields; p-adic L-functions Deligne, Pierre; Ribet, Kenneth A., Values of abelian {\(L\)}-functions at negative integers over totally real fields, Inventiones Mathematicae, 59, 227-286, (1980) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sum of squares; positive polynomial; convex set; Caratheodory's convex hull theorem Naldi, Simone, Nonnegative polynomials and their Carathéodory number, Discrete comput. geom., 51, 3, 559-568, (2014) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) survey article (algebraic geometry); algebraic curves; Brill-Noether theory; moduli spaces of curves; Hilbert schemes; special divisors; linear systems | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) biographies; Oscar Zariski; algebraic geometry; schools of mathematics; algebraic surfaces; singularity theory; linear systems C. Parikh, The unreal life of Oskar Zariski, Springer, 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) tangential Hilbert 16th problem; isolated ovals of algebraic level curves; differential algebraic generalization D. Novikov and S. Yakovenko, ''Tangential Hilbert Problem for Perturbations of Hyperelliptic Hamiltonian Systems,'' Electron. Res. Announc. Am. Math. Soc. 5(8), 55--65 (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) explicit class field theory; real quadratic fields; quaternion algebras; Shimura 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) Artin-Schreier-Witt theory; Witt group scheme; Frobenius map; Galois extensions; u-cyclic \(p^ n\)-extensions; Hopf algebras | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) curve over a global field; \(K_1\); local class field theory of curves; Galois cohomology; surfaces over finite fields Wayne Raskind, On \?\(_{1}\) of curves over global fields, Math. Ann. 288 (1990), no. 2, 179 -- 193. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Witt ring; real spectrum; KO; K-theory; ring of abstract semi-algebraic functions G. W. Brumfiel, Witt rings and \?-theory, Rocky Mountain J. Math. 14 (1984), no. 4, 733 -- 765. Ordered fields and real algebraic geometry (Boulder, Colo., 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) moving cuspidal singularities; positive characteristic; fibration by p- closed rational vector fields; singularities of fibres; generalized Raynaud surface Takeda, Y.: Fibrations with moving cuspidal singularities. Nagoya Math. J.122, 161-179 (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) differentially closed fields; model theory; diophantine geometry; survey; Mordell-Lang conjecture Marker, D.: Model theory of differential fields. In: Model theory, algebra, and geometry, \textit{Mathematical Sciences Research Institute Publications}, vol.~39, pp. 53-63. Cambridge University Press, Cambridge (2000). http://library.msri.org/books/Book39/files/dcf.pdf | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 stability; Chow weight; geometric invariant theory; Hilbert-Mumford criterion; moduli 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) \(G\)-functions; formal power series; linear differential equation; \(p\)- adic differential equations; Padé approximants; general introduction to \(p\)-adic analysis; Dwork's theorem; rationality of the zeta function of a hypersurface over a finite field; \(D\)-modules; Honda's theory of differential equations in finite characteristics; applications to Katz' theorem; Dwork-Robba theorem; Dwork's transfer principles; Chudnovsky's theorem; Dwork-Robba type estimates; growth of solutions at the boundary of a singular disk; nilpotent monodromy; diophantine nature of the exponents; equivalence of Bombieri's and Galochkin's conditions B. \textsc{Dwork}, G. \textsc{Gerotto} and F. \textsc{Sullivan}, \textit{An Introduction to G-Functions}, Annals of Mathematical Studies, vol.~133, Princeton University Press, Princeton, 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) first order theory of function fields in the language of fields; curves; undecidability Jean-Louis Duret, Sur la théorie élémentaire des corps de fonctions, J. Symbolic Logic 51 (1986), no. 4, 948 -- 956. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 systems theory; scattering; filtering; pole-placement; linear input-output system; Heaviside-Mikusinski theory of differential fields and operators; Kronecker pencil Hermann, R.: Topics in the geometric theory of linear systems. Interdisciplinary mathematics (1984) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) singularities of mappings; Thom-Mather theory; nice dimensions; right-left equivalence; contact equivalence; stability; versal unfoldings; finite determinacy; vector fields and flows; local conical structure; Thom-Boardman singularities; topological stability; unstable map-germs; unipotent algebraic groups; critical space; discriminants; bifurcation sets; isosingular locus; logarithmic tangent space; logarithmic transversality; stable perturbations; disentanglement of a map; image Milnor numbers; discriminant Milnor numbers; free and almost free divisors; complete intersections; Fitting ideals; conductor ideals; multiple point spaces; knot theory; Reidemeister moves; rank condition; parameterised hypersurfaces; maximal Cohen-Macaulay modules; duality; Gorenstein rings; canonical module; triple 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) p-adically closed fields; definable closed sets; quantifier elimination; p-adic fields; sets of n-th powers; model completion DOI: 10.1016/0021-8693(87)90041-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) Diffie-Hellman key exchange; discrete logarithm problem; real quadratic congruence function fields; elliptic curves Andreas Stein, Equivalences between elliptic curves and real quadratic congruence function fields, J. Théor. Nombres Bordeaux 9 (1997), no. 1, 75 -- 95 (English, with English and French summaries). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 solutions; enumerative problem; Schubert subvarieties of Grassmannians Chiavacci, R.; Escamilla-Castillo, J.: Schubert calculus and enumerative problems. Bollettino U.M.I. 7, No. 2-A, 119-126 (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) meromorphic functions; number field analogue of Nevanlinna's five-valued theorem counting multiplicities; uniqueness polynomials for complex meromorphic functions; non-Archimedean meromorphic functions; algebraic function fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive semi-definite polynomials; sums of squares; semi-algebraic sets Ch. Ferrier, Hubert's 17th problem and best dual bounds in quadratic minimization. Cybernetics and System Analysis 5 ( 1998) 76-91. Zbl0972.13017 MR1712046 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Thom's lemma; coding of real algebraic numbers; cylindric algebraic decomposition of a semialgebraic set 8. M. COSTE et M.-F. ROY, Thom's Lemma, the Coding of Real Algebraic Numbers and the Computation of the Topology of Semi-AIgebraic Sets, J. Symbolic Computations, 1988, 5, p. 121-129. Zbl0689.14006 MR949115 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) supersymmetry; topological strings; \(tt^*\) geometry; twistorial extensions; Riemann-Hilbert problem; Liouville theory; matrix models S. Cecotti, A. Neitzke and C. Vafa, \textit{R-Twisting and 4d/2d Correspondences}, arXiv:1006.3435 [INSPIRE]. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Drinfeld modules; elliptic modules; cyclotomic function fields; congruence function fields; Carlitz modules; nonarchimedean analysis; explicit class field theory; Gauss sums; Gamma and Zeta functions and values; Jacobi sums; diophantine approximation; \(t\)-modules; \(t\)-motives; transcendence and irrationality; automata and algebraicity D.S. Thakur, \(Function Field Arithmetic\), World Scientfic, Singapore, 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) positive polynomials; sums of squares Schmüdgen K. Around Hilbert's 17th problem, \textit{Documenta Mathematica}, extra volume: optimization stories. 2012. pp. 433-438. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 subset problem; yin-yang symbol; bisection of yin-yang; perfect set; borderline between yin-yang; reflection symmetry; disclosing symmetry within disk; Fermat's spiral; \(n\)-part yin-yang symbols | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Paris (France); Journée; Géometrie algébrique réelle; Descartes; Fourier; Sturm; Tarski; Seidenberg; algebraic geometry; Bezout's theorem; Hilbert's 16th problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Gál's sums; Dirichlet polynomials; Riemann zeta function; Dirichlet \(L\)-functions; resonance method; function fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) combinatorial root count; control theory; dynamic pole placement problem; enumerative geometry; Grassmannian; numerical Schubert calculus; Pieri homotopy; quantum Schubert calculus Huber B., SIAM J. Control Optim. 38 (4) pp 1265-- (2000) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Campana's conjectures; function fields; Nevanlinna theory; orbifolds; hyperbolicity | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 knot theory; encomplexed writhe; topology of real algebraic varieties Björklund, J., Real algebraic knots of low degree, J. Knot Theory Ramification, 20, 1285, (2011) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive polynomials; sums of squares; semi-algebraic functions Murray, M; Tim, N, Positivstellensätze for real function algebras, Math. Z., 270, 889-901, (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's 14-th problem Klaus Pommerening, Invariants of unipotent groups. A survey, Invariant theory, Lecture Notes in Math., vol. 1278, Springer, Berlin, 1987, pp. 8 -- 17. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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-commutative deformation theory; time-space; dirac derivation; phase space; non-commutative scheme; representations of associative algebras; dynamical structure; interaction; algebraic quantum fields; connections | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algorithm; effective version of Hilbert's Nullstellensatz; Taylor formulas; Positivstellensatz | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) affine Nash manifold; complexity of Nash functions; Tarski-Seidenberg principle; real spectrum; separation problem Coste, M; Ruiz, JM; Shiota, M, Uniform bounds on complexity and transfer of global properties of Nash functions, J. Reine Angew. Math., 536, 209-235, (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) plane curves; bitangents; determinantal representations; sums of squares; semidefinite programming; Gale duality Plaumann, D., Sturmfels, B., Vinzant, C.: Quartic curves and their bitangents. J. Symb. Comput. \textbf{46}(6), 712-733 (2011) (14H50 (14N05)) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) normal basis; optimal normal bases; elliptic curves over finite fields; elliptic curve cryptosystems; codes; finite fields; finite field arithmetic; factoring of polynomials; discrete logarithm problem; irreducible polynomials; survey Menezes, A. J., Blake, I. F., Gao, X., Mullin, R. C., Vanstone, S. A., \& Yaghoobian, T. (1993). Applications of finite fields. Kluwer international series in engineering and computer science. ISBN: 0-7923-9282-5. | 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) space of sums of powers; Waring decomposition; real rank; variety of sums of powers Michałek, Mateusz; Moon, Hyunsuk, Spaces of sums of powers and real rank boundaries, (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) abelian varieties; Lehmer's problem; Néron-Tate height; complex multiplication; rational points; number fields; zero estimates David, S; Hindry, M, Minoration de la hauteur de Néron-Tate sur LES variétés abéliennes de type C.M, J. Reine Angew. Math., 529, 1-74, (2000) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(a\)-numbers; Artin-Schreier covers; arithmetic geometry; covers of curves; invariants 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) sums of squares; convexity; bitangents; faces; ternary quartics; Gram spectrahedron | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(p\)-adic fields; differential character; abelian scheme; theorem of the kernel; arithmetic jet theory Buium, Alexandru, Differential characters of abelian varieties over \textit{p}-adic fields, Invent. Math., 122, 1, 309-340, (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) Mickelsson-Faddeev cocycle; existence of string structures; bundle gerbe; quantum field theory; Atiyah-Patodi-Singer index theory; bundle of fermionic Fock spaces; gauge group action; Dixmier-Douady class; fermions in external fields; APS theorem; WZW model; Riemann surfaces; global Hamiltonian anomalies A. Alan Carey, A. Mickelsson, and M. Murray, ''Bundle gerbes applied to quantum field theory,'' hep-th/9711133. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) adjoint quotient; stratified Kähler space; Poisson manifold; Poisson algebra; Poisson cohomology; holomorphic quantization; reduction and quantization; geometric quantization; quantization on a space with singularities; normal complex analytic space; locally semialgebraic space; constrained system; invariant theory; bisymmetric functions; multisymmetric functions; quantization in the presence of singularities; costratified Hilbert space Huebschmann, J.: Stratified Kähler structures on adjoint quotients | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S.J. (1988). An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Studies in Advanced Mathematics 14 . Cambridge: Cambridge Univ. Press. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) linear nested Artin approximation theorem; formal power series; problem of the commutation of two operation | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 quotient; Hilbert quotient; moduli of curves; phylogenetic trees; geometric invariant theory; toric geometry; tropical geometry Gibney, A., Maclagan, D.: Equations for Chow and Hilbert quotients. Algebra Number Theory. \textbf{7}, 855-885 (2010). arXiv:0707.1801 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) simultaneous zeros; quadratic forms; cubic forms; p-adic fields; Artin'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) Bibliography; moduli spaces of algebraic curves; Hilbert schemes; stable algebraic curves; Deligne-Mumford compactification; Brill-Noether theory; geometric invariant theory; families of curves J. Harris, I. Morrison, \textit{Moduli of curves}. Springer 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) diophantine equations; Siegel's theorem; integral points on affine curves; function-fields of characteristic zero José Felipe Voloch, Siegel's theorem for complex function fields, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1307 -- 1308. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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; coordinate ring; affine plane curve; explicit representation; 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) certificates of non-negativity; sums of squares; degree bounds | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) summatory functions; divisor function; number of representations as sums of squares; incomplete exponential sums; conditional asymptotic results; arithmetic functions; arithmetic progression | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) constructible set; algebraically closed fields; definability; quantifier elimination procedure; time bound; prenex first order formulas; Bezout's theorem J. Heintz, \textit{Definability and fast quantifier elimination in algebraically closed fields}, Theoret. Comput. Sci. \textbf{24} (1983), no. 3, 239-277. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Whitney's closed umbrella; relaxation type oscillator; bundles of binomial surfaces A. A. Davydov, ''The Normal Form of Slow Motions of an Equation of Relaxation Type and Fibrations of Binomial Surfaces,'' Mat. Sb. 132(1), 131--139 (1987) [Math. USSR, Sb. 60 (1), 133--141 (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) evaluation of cubic character sums; Legendre symbol; elliptic curves with complex multiplication; Frobenius automorphism; formula for multiplication by \(\sqrt{-3}\) Dimitrios Poulakis, Évaluation d'une somme cubique de caractères, J. Number Theory 27 (1987), no. 1, 41 -- 45 (French). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) second Chern class; Yang-Mills fields; Donaldson theory; Atiyah-Jones conjecture; topological Euler characteristics of the moduli spaces | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) homotopy invariant pseudo pretheory; extensions of algebraically closed fields Rosenschon, A.; Østvær, P. A., Rigidity for pseudo pretheories, Invent. Math., 166, 1, 95-102, (2006), MR 2242633 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Chisini's problem; projective surface; Picard-Lefschetz theory; braid 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) Hilbert modular form; Shimura variety; Iwasawa theory; Galois deformation ring; Hecke algebra; \({\mathcal L}\)-invariant; basis problem Hida H., Hilbert modular forms and Iwasawa theory, Clarendon Press, Oxford 2006. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) towers of function fields; rational points; finite fields; hypergeometric functions; Deuring's polynomial Hasegawa, On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric functions, Int. J. Number Theory 6 pp 989-- (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) function fields; irreducible polynomials; hyperelliptic curves; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; 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) \(\ell\)-adic cohomology; independence of \(\ell \); grothendieck's trace formula; Lefschetz trace formula; zeta functions over finite fields; Euler-poincaré characteristic; Betti number; bloch's conductor conjecture; intersection cohomology; grothendieck's six operations; intermediate extension; Weil conjectures; Hodge polygon; Newton polygon; crystalline cohomology; Hodge filtration; coniveau filtration; alteration; Fano variety; rationally connected; Weil group; swan conductor; wild ramification; Brauer trace; log scheme; logarithmic differential forms; Čebotarev's density theorem; semisimple group; fatou's Lemma Illusie, L.: Miscellany on traces in \(\mathcall \)-adic cohomology: a survey. Japan J. Math. \textbf{1}(1), 107-136 (2006). Erratum: Japan J. Math. \textbf{2}(2), 313-314 (2007) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 theory; representations of finitely generated groups; algebraic group; variety; real points; lattice; semisimple Lie group; fundamental group; compact Kähler manifold; monodromy representation; polarized Hodge structure; Margulis superrigidity theorem; hyperbolic manifolds; totally geodesic hypersurfaces; flat connections J.J. Millson. Deformations of Representations of finitely Generated Groups. Contemp. Math.74, 237-253 (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) MMP; real algebraic threefolds; minimal model; flips; divisorial contractions; factorization problem of birational morphisms János Kollár, Real algebraic threefolds. II. Minimal model program, J. Amer. Math. Soc. 12 (1999), no. 1, 33 -- 83. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) hyper-Kähler manifold; twistor coordinates; variations of BPS structures; conformal limit; Riemann-Hilbert 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) basic semialgebraic set; piecewise-polynomial functions; polynomial functions; real analytic functions; transversal zeros theorem; germs of real analytic functions; basic closed seminanalytic set Delzell, C. N.: Non-existence of analytically varying solutions to Hilbert's 17th problem. Contemp. math. 155, No. 73, 107-117 (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) Serre's problem; moduli spaces; arrangements of lines; linkages in the Euclidean plane M. Kapovich and J. Millson, ''Moduli spaces of linkages and arrangements,'' Prog. Math. 172,730--770 (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) curves of genus two; descent theory; geometric Galois theory; Brumer's family; Humbert's modular equation; Poncelet's pentagon; algebraic correspondences Hashimoto, [Hashimoto 00] K., On Brumer's family of RM-curves of genus two, \textit{Tohoku Math. J. (2)}, 52, 4, 475-488, (2000) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic cycles; Chow groups; motives; Bloch's conjecture; Bloch-Beilinson filtration; hyperkähler varieties; \(K3\) surfaces; Hilbert schemes; non-symplectic involution; multiplicative Chow-Künneth decomposition; ``spread'' of algebraic cycles in a family | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) uniformly locally finite triangulation; complex projective varieties with conical singularities; real cohomology group; canonical combinatorical Laplace operator; open manifolds; infinite simplicial complexes; \(L_ 2\)-cohomology; Sobolev cohomology; analytical \(L_ 2\)-cohomology of open oriented Riemannian manifolds; de Rham-Hodge isomorphism in the \(L_ 2\)- category; Hirzebruch's conjecture; intersection homology | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 polynomial; sum of squares; free algebra; real algebraic geometry; *-algebra Jakob Cimprič, Noncommutative Positivstellensätze for pairs representation-vector, Positivity 15 (2011), no. 3, 481 -- 495. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) discriminant of splitting fields of principal homogeneous spaces; finiteness for the Tate-Shafarevich group of an elliptic curve; Arakelov intersection theory; effective divisor; Faltings Riemann-Roch theorem Paul Hriljac, Splitting fields of principal homogeneous spaces , Number theory (New York, 1984-1985), Lecture Notes in Math., vol. 1240, Springer, Berlin, 1987, pp. 214-229. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) inverse problem of Galois theory, algebraic function field; arithmetic fundamental group; algebraic fundamental group; special linear group; SL(2,q); Mathieu group; \(M_{12}\); \(M_{22}\) Matzat, B.H.: Zwei Aspekte konstruktiver Galoistheorie,J. Algebra 96 (1985), 499--531 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) noncommutative tori; real multiplication; Stark numbers; real quadratic fields; spectral triples; noncommutative boundary of modular curves; modular shadows; quantum statistical mechanics | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) abelian integral; hyperbolic curve; weakened Hilbert's 16th problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) semialgebraic sets; semidefinite programming; moment relaxations; polynomial sums of squares V. Magron, D. Henrion, and J.-B. Lasserre, \textit{Semidefinite approximations of projections and polynomial images of semialgebraic sets}, SIAM J. Optim., 25 (2015), pp. 2143--2164, . | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) construction; curves over finite fields; characteristic 2; supersingular curves; coding theory; generalized Hamming weights; odd characteristics; number of parameters G. VAN DER GEER - M. VAN DER VLUGT, On the existence of supersingular curves of given genus, J. Reine Angew. Math., 458 (1995), pp. 53-61. Zbl0819.11022 MR1310953 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 structures; linearly ordered structure; ordered vector space; real closed field; differentiable structure Peterzil, Y., and S. Starchenko, ''A trichotomy theorem for o-minimal structures'', Proceedings of the London Mathematical Society , Third Series, vol. 77 (1998), pp. 481--523. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) unit group of group algebra; group scheme; cyclic group of prime power order; Kummer-Artin-Schreier-Witt theories T. Sekiguchi and N. Suwa, On the structure of the group scheme \(\z[\z/p^n]^\times\), Compositio Math., 97 (1995), 253-271. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's fourteenth problem; derivations DOI: 10.4064/ap76-1-9 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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; finiteness theorems; hyperbolic manifolds; rational points; integer points; finite modulo trace; loops on complex manifolds; closed points on algebraic varieties over a finite field A. N. Parshin, ``Finiteness theorems and hyperbolic manifolds'', The Grothendieck Festschrift. A collection of articles written in honor of the 60th birthday of Alexander Grothendieck, v. III, Progr. Math., 88, Birkhaüser, Boston, MA, 1990, 163 -- 178 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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; spectrahedra; free resolutions; Castelnuovo-Mumford regularity Blekherman, G.; Sinn, R.; Velasco, M., Do sums of squares dream of free resolutions?, SIAM J. Appl. Algebra Geom., 1, 175-199, (2017) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Viro's theorem; real algebraic set; complete intersections; mixed decompositions of Newton polytopes; number of real points B. Sturmfels, \textit{Viro's theorem for complete intersections}, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 21 (1994), pp. 377--386. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 rank; strength; Schmidt rank; perfect field; extension of fields; polynomials; additive character; \(p\)-adic ring; Nullstellensatz over a non-closed field; \(p\)-adic bias rank | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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; Gram spectrahedra; face; binary form; 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) real algebraic surfaces; Betti numbers; Viro method; sixteenth Hilbert problem Bihan, F., Asymptotic Behaviour of Betti Numbers of Real Algebraic Surfaces, Comment. Math. Helv., 2003, vol. 78, pp. 227--244. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) bifurcation of relative equilibria; Newtonian 4-body problem; algebraic correspondence between real algebraic varieties R. Moeckel, ''Relative equilibria of the four-body problem,'' Ergodic Theory Dynam. Systems, vol. 5, iss. 3, pp. 417-435, 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) universal completion of morphism; real closed spaces | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algorithmic; Positivstellensatz; Hilbert Nullstellensatz; formally real 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) zero estimates of transcendence theory on a commutative algebraic group; periods; Abelian varieties; tori; Hilbert polynomials; Riemann-Roch theorem; lattices; Minkowski theorem Bertrand, D.; Philippon, P.: Sous-groupes algébriques de groupes algébriques commutatifs. Illinois J. Math. 32, 263-280 (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) inverse problem of Galois theory; rational variety; connectedness of the Nielsen class; rigidity of the group FRIED, M.: On reduction of the inverse Galois group problem to simple groups. Erscheint demn?chst | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered 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 with many points; number of rational points; quadratic forms; fibre products; Artin-Schreier curves; trace codes; arbitrary characteristic; \(C_{ab}\) 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) group scheme; algebraic group; albanese morphism; Hilbert's fourteenth problem Séminaire de Géométrie Algébrique du Bois Marie 1960-61: Revêtements étales et groupe fondamental (SGA 1). Séminaire dirigé par A. Grothendieck. Augmenté de deux exposés de Mme M. Raynaud. Documents Mathématiques, vol. 3. Soc. Math. France, Paris (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) circle method; function fields; diagonal hypersurfaces; Vinogrador's mean value theorem; Waring's problem Zhao, X.: Asymptotic estimates for rational spaces on hypersurfaces in function fields, Proc. lond. Math. soc. (3) 104, 287-322 (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) Artin-Schreier-Witt theory; torsors; degeneration; group schemes Mohamed Saïdi, On the degeneration of étale \?/\?\? and \?/\?²\?-torsors in equal characteristic \?>0, Hiroshima Math. J. 37 (2007), no. 2, 315 -- 341. | 0 |
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