This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.
| ISBN: | 9781107462496 |
| Publication date: | 13th August 2015 |
| Author: | G O University of Manchester Jones |
| Publisher: | Cambridge University Press |
| Format: | Paperback |
| Pagination: | 234 pages |
| Series: | London Mathematical Society Lecture Note Series |
| Genres: |
Number theory Set theory Mathematical logic |
This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.
O-Minimality and Diophantine Geometry features in the following genres: Number theory, Set theory, Mathematical logic
O-Minimality and Diophantine Geometry is available in Paperback
O-Minimality and Diophantine Geometry was written by G O University of Manchester Jones and published by Cambridge University Press
O-Minimality and Diophantine Geometry has 234 pages
Yes it is part of London Mathematical Society Lecture Note Series series