Some Problems of Unlikely Intersections in Arithmetic and Geometry

Descripción

This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the Andre-Oort conjecture (outlining work by Pila).

N° de ref. del artículo LU-9780691153711

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Detalles bibliográficos

Título

Some Problems of Unlikely Intersections in Arithmetic and Geometry

Editor

Princeton University Press

Fecha de publicación

2012

Idioma

Inglés

ISBN 10

069115371X

ISBN 13

9780691153711

Encuadernación

Paperback

Estado

New

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