O-Minimality and Diophantine Geometry
Book Details
Format
Paperback / Softback
Book Series
London Mathematical Society Lecture Note Series
ISBN-10
1107462495
ISBN-13
9781107462496
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Aug 13th, 2015
Print length
234 Pages
Weight
350 grams
Dimensions
15.50 x 22.90 x 1.80 cms
Product Classification:
Mathematical logicSet theoryNumber theory
Ksh 11,350.00
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This collection of articles brings the researcher up to date with recent applications of logic, specifically model theory, to conjectures associated with those of Manin–Mumford and André–Oort. Originating from a short course, it combines original papers with background articles on related topics.
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.
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