Some Problems of Unlikely Intersections in Arithmetic and Geometry by Umberto Zannier
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).-
Seminar on the Atiyah-Singer Index Theorem
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The Master Equation and the Convergence Problem in Mean Field Games
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Lectures on Curves on an Algebraic Surface
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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik
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The Einstein-Klein-Gordon Coupled System
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A Hierarchy of Turing Degrees
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Elementary Differential Topology
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An Introduction to G-Functions
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The Norm Residue Theorem in Motivic Cohomology
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The Structure of Groups with a Quasiconvex Hierarchy
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Curvature and Betti Numbers
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Period Spaces for p-divisible Groups
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Exponential Sums and Differential Equations
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Functional Operators, Volume 2
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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
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The Decomposition of Global Conformal Invariants
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Weyl Group Multiple Dirichlet Series
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Green's Function Estimates for Lattice Schroedinger Operators and Applications. (AM-158)
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Automata Studies
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Arithmetic and Geometry
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Stationary Processes and Prediction Theory
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Seminar on Singularities of Solutions of Linear Partial Differential Equations
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Contributions to Fourier Analysis
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Unipotent Ideals and Harish-Chandra Bimodules
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Hoelder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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Non-Archimedean Tame Topology and Stably Dominated Types
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The p-adic Simpson Correspondence
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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
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Contributions to the Theory of Games, Volume IV
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Seminar on Micro-Local Analysis
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Contributions to the Theory of Games, Volume II
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Euler Systems
"Zannier's book is well written and a pleasure to read.. [T]he author always makes an effort to point out key ideas and key steps, so a reader who wants to read and understand the complete proofs in this technically demanding field will find this monograph to be an extremely helpful entree into the subject... [T]he reviewer highly recommends Zannier's book as an excellent survey of and introduction to the important and hot topic of unlikely intersections in arithmetic geometry."--Joseph H. Silverman, Bulletin of the AMS "This book is indeed a great source of knowledge and inspiration for everybody interested in the unlikely intersection problems. The author must be commended for doing this job, and doing it so well."--Yuri Bilu, Mathematical Reviews Clippings
Umberto Zannier is professor of mathematics at the Scuola Normale Superiore di Pisa in Pisa, Italy. He is the author of Lecture Notes on Diophantine Analysis and the editor of Diophantine Geometry.
| SKU | Unavailable |
| ISBN 13 | 9780691153704 |
| ISBN 10 | 0691153701 |
| Title | Some Problems of Unlikely Intersections in Arithmetic and Geometry |
| Author | Umberto Zannier |
| Series | Annals Of Mathematics Studies |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Princeton University Press |
| Year published | 2012-03-25 |
| Number of pages | 176 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |