O-Minimality and Diophantine Geometry

G. O. Jones · A. J. Wilkie

2015年8月 · London Mathematical Society Lecture Note Series 第 421 冊 · Cambridge University Press

電子書

235

頁

評分和評論未經驗證瞭解詳情

關於本電子書

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.

關於作者

A. J. Wilkie is the Fielden Professor of Pure Mathematics at the University of Manchester. He has twice been joint winner of the Association for Symbolic Logic's Karp Prize. He is a Fellow of the Royal Society, of the American Mathematical Society and a member of Academia Europaea. Wilkie recently served as President of the Association for Symbolic Logic from 2010 to 2013.

G. O. Jones is a Researcher in the School of Mathematics at the University of Manchester.