Hilbert's tenth problem : relations with arithmetic and algebraic geometry / [electronic resource] Jan Denef ... [et al.], editors. - Providence, R.I. : American Mathematical Society, c2000. - 1 online resource (xii, 367 p.) - Contemporary mathematics, v. 270 0271-4132 (print); 1098-3627 (online); . - Contemporary mathematics (American Mathematical Society) ; v. 270. .

Includes bibliographical references.

Hilbert's tenth problem: what was done and what is to be done / Undecidability of existential theories of rings and fields: a survey / 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 $$ 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 / 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 / Yuri Matiyasevich -- Thanases Pheidas and Karim Zahidi -- Alexandra Shlapentokh -- Mihai Prunescu -- L. Darni�ere -- Laurent Moret-Bailly -- Joachim Schmid -- Moshe Jarden and Aharon Razon -- Thanases Pheidas -- Gunther Cornelissen and Karim Zahidi -- Paul Vojta -- J. Maurice Rojas -- Anand Pillay -- K. H. Kim and F. W. Roush -- Curtis D. Bennett, Lisa K. Elderbrock and Andrew M. W. Glass -- http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04368 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04369 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04370 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04371 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04372 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04373 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04374 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04375 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04376 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04377 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04378 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04379 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04380 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04381 http://www.ams.org/conm/270/ http://dx.doi.org/10.1090/conm/270/04382

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Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.

Mode of access : World Wide Web

9780821878606 (online)

Hilbert's tenth problem.
Arithmetical algebraic geometry.
Geometry, Algebraic.

QA242 / .H55 2000

The Institute of Mathematical Sciences, Chennai, India

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