Hilbert's tenth problem : diophantine classes and extensions to global fields
Alexandra Shlapentokh.
Cambridge : Cambridge University Press, 2007.
xiii, 320 págs. ; 24 cm.
Serie: New mathematical monographs ; 7
ISBN: 0521833604 (cased), 9780521833608 (cased)
Incluye referencias bibliográficas e índice.
Reseña: MathSciNet, 2009e:11235
Contenido
- 1. Introduction
- 2. Diophantine classes: definition and basic facts
- 3. Diophantine equivalence and diophantine decidability
- 4. Integrality at finitely many primes and divisibility of order at infinitely many primes
- 5. Bound equations for number fields and their consequences
- 6. Units of rings of W-integers of norm 1
- 7. Diophantine classes over number fields
- 8. Diophantine undecidability of function fields
- 9. Bounds for function fields
- 10. Diophantine classes over function fields
- 11. Mazur's conjectures and their consequences
- 12. Results of Poonen
- 13. Beyond global fields
- A. Recursion theory
- B. Number theory.
