(DOWNLOAD) "O-Minimality and Diophantine Geometry" by G. O. Jones # eBook PDF Kindle ePub Free

May 22, 2021

eBook details

Title: O-Minimality and Diophantine Geometry
Author : G. O. Jones
Release Date : January 31, 2015
Genre: Mathematics,Books,Science & Nature,
Pages : * pages
Size : 4112 KB

Description

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.