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# Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry

### About this Title

**Jan Denef**, **Leonard Lipshitz**, **Thanases Pheidas** and **Jan Van Geel**, Editors

Publication: Contemporary Mathematics

Publication Year:
2000; Volume 270

ISBNs: 978-0-8218-2622-5 (print); 978-0-8218-7860-6 (online)

DOI: https://doi.org/10.1090/conm/270

MathSciNet review: 1802007

### Table of Contents

**Download chapters as PDF**

**Front/Back Matter**

**Articles**

- Yuri Matiyasevich – Hilbert’s tenth problem: what was done and what is to be done [MR 1802008]
- Thanases Pheidas and Karim Zahidi – Undecidability of existential theories of rings and fields: a survey [MR 1802009]
- Alexandra Shlapentokh – Hilbert’s tenth problem over number fields, a survey [MR 1802010]
- Mihai Prunescu – Defining constant polynomials [MR 1802011]
- L. Darnière – Decidability and local-global principles [MR 1802012]
- Laurent Moret-Bailly – Applications of local-global principles to arithmetic and geometry [MR 1802013]
- Joachim Schmid – Regularly $T$-closed fields [MR 1802014]
- Moshe Jarden and Aharon Razon – Skolem density problems over large Galois extensions of global fields [MR 1802015]
- Thanases Pheidas – An effort to prove that the existential theory of $\textbf {Q}$ is undecidable [MR 1802016]
- Gunther Cornelissen and Karim Zahidi – Topology of Diophantine sets: remarks on Mazur’s conjectures [MR 1802017]
- Paul Vojta – Diagonal quadratic forms and Hilbert’s tenth problem [MR 1802018]
- J. Maurice Rojas – Algebraic geometry over four rings and the frontier to tractability [MR 1802019]
- Anand Pillay – Some model theory of compact complex spaces [MR 1802020]
- K. H. Kim and F. W. Roush – Double coset decompositions for algebraic groups over $K[t]$ [MR 1802021]
- Curtis D. Bennett, Lisa K. Elderbrock and Andrew M. W. Glass – Zero estimates for polynomials in 3 and 4 variables using orbits and stabilisers [MR 1802022]