04376nam 2200637 450 991048030910332120170821165834.00-8218-7860-30-8218-5606-5(CKB)3240000000069797(EBL)3112887(SSID)ssj0000850344(PQKBManifestationID)11418975(PQKBTitleCode)TC0000850344(PQKBWorkID)10832345(PQKB)10807085(MiAaPQ)EBC3112887(WaSeSS)Ind00039403(PPN)197105955(EXLCZ)99324000000006979720001026h20002000 uy| 0engur|n|---|||||txtccrHilbert's tenth problem relations with arithmetic and algebraic geometry : Workshop on Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry, November 2-5, 1999, Ghent University, Belgium /Jan Denef [and three others], editorsProvidence, Rhode Island :American Mathematical Society,[2000]©20001 online resource (384 p.)Contemporary mathematics,0271-4132 ;270Description based upon print version of record.0-8218-2622-0 Includes bibliographical references.""Contents""; ""Introduction""; ""List of Participants""; ""Hilbert's tenth problem: What was done and what is to be done""; ""Undecidability of existential theories of rings and fields: A survey""; ""1. Introduction""; ""2. The existential theory of rational function fields""; ""3. The existential theory of algebraic function fields""; ""4. A geometric analogue of Hilbert's Tenth Problem""; ""5. Decision problems concerning rings of analytic functions: introduction""; ""6. First-order theories of rings of analytic functions""""7. Existential decidability and the Approximation Property for rings of analytic functions""""8. Existential undecidability for rings of analytic functions""; ""9. Polynomial rings and p-adic entire functions""; ""10. Existential theories of fields of meromorphic functions""; ""11. Variations: Languages with predicates for symmetric functions""; ""Appendix A. Elliptic curves: Basic Definitions""; ""Appendix B. Elliptic curves over function fields""; ""Appendix C. Pell equations""; ""References""; ""Hilbert's tenth problem over number fields, a survey""; ""Defining constant polynomials""""Decidability and local-global principles""""Applications of local-global principles to arithmetic and geometry""; ""Regularly T-closed fields""; ""Skolem density problems over large Galois extensions of global fields""; ""An effort to prove that the existential theory of Q is undecidable""; ""Topology of diophantine sets: Remarks on Mazur's conjectures""; ""Diagonal quadratic forms and Hilbert's tenth problem""; ""Algebraic geometry over four rings and the frontier to tractability""; ""1. Introduction""; ""2. Computing Complex Dimension Faster""""3. Polytope Volumes and Counting Pieces of Semi-Algebraic Sets""""4. The Generalized Riemann Hypothesis and Detecting Rational Points""; ""5. Effective Siegel Versus Detecting Integral Points on Surfaces""; ""6. Proofs of Our Main Technical Results""; ""7. Acknowledgements""; ""Appendix: How the Examples Were Computed""; ""References""; ""Some model theory of compact complex spaces""; ""Double coset decompositions for algebraic groups over K[t]""; ""Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers""Contemporary mathematics (American Mathematical Society) ;270.Hilbert's tenth problemArithmetical algebraic geometryGeometry, AlgebraicElectronic books.Hilbert's tenth problem.Arithmetical algebraic geometry.Geometry, Algebraic.512/.7Denef Jan1951-Workshop on Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry(1999 :Ghent University, Belgium),MiAaPQMiAaPQMiAaPQBOOK9910480309103321Hilbert's tenth problem1424549UNINA