O-Minimality and Diophantine Geometry
G. O. Jones ¡ A. J. Wilkie
āĻāĻ ā§¨ā§Ļā§§ā§Ģ ¡ London Mathematical Society Lecture Note Series āĻŦāĻ 421 ¡ Cambridge University Press
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This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the AndreâOort conjecture for products of modular curves. The basic strategy has three main ingredients: the PilaâWilkie 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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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.
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