Point Counting And The Zilber Pink Conjecture PDF Download
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Author | : Jonathan Pila |
Publisher | : Cambridge University Press |
Total Pages | : 268 |
Release | : 2022-06-09 |
Genre | : Mathematics |
ISBN | : 1009301926 |
Download Point-Counting and the Zilber–Pink Conjecture Book in PDF, ePub and Kindle
Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.
Author | : Jonathan Pila |
Publisher | : |
Total Pages | : |
Release | : 2022 |
Genre | : MATHEMATICS |
ISBN | : 9781009170314 |
Download Point-counting and the Zilber-Pink Conjecture Book in PDF, ePub and Kindle
Author | : János Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 491 |
Release | : 2023-04-30 |
Genre | : Mathematics |
ISBN | : 1009346105 |
Download Families of Varieties of General Type Book in PDF, ePub and Kindle
The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Author | : D. E. Edmunds |
Publisher | : Cambridge University Press |
Total Pages | : 169 |
Release | : 2022-10-31 |
Genre | : Mathematics |
ISBN | : 1009254634 |
Download Fractional Sobolev Spaces and Inequalities Book in PDF, ePub and Kindle
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Author | : Shmuel Weinberger |
Publisher | : Cambridge University Press |
Total Pages | : 365 |
Release | : 2022-11-30 |
Genre | : Mathematics |
ISBN | : 1107142598 |
Download Variations on a Theme of Borel Book in PDF, ePub and Kindle
Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.
Author | : Alejandro D. de Acosta |
Publisher | : |
Total Pages | : 264 |
Release | : 2022-10-12 |
Genre | : Mathematics |
ISBN | : 1009063359 |
Download Large Deviations for Markov Chains Book in PDF, ePub and Kindle
This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Author | : G. O. Jones |
Publisher | : Cambridge University Press |
Total Pages | : 235 |
Release | : 2015-08-20 |
Genre | : Mathematics |
ISBN | : 1316301060 |
Download O-Minimality and Diophantine Geometry Book in PDF, ePub and Kindle
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.
Author | : Umberto Zannier |
Publisher | : Princeton University Press |
Total Pages | : 175 |
Release | : 2012-03-25 |
Genre | : Mathematics |
ISBN | : 1400842719 |
Download Some Problems of Unlikely Intersections in Arithmetic and Geometry Book in PDF, ePub and Kindle
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 André-Oort conjecture (outlining work by Pila).
Author | : Philipp Habegger |
Publisher | : |
Total Pages | : 0 |
Release | : 2017 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9782856298565 |
Download Around the Zilber-Pink Conjecture Book in PDF, ePub and Kindle
"Following Faltings and Vojta's work proving the Mordell-Lang conjecture for abelian varieties and Raynaud's work proving the Manin-Mumford conjecture, many new diophantine questions appeared, often described as problems of unlikely intersections. The arithmetic of moduli spaces of abelian varieties and, more generally, Shimura varieties has been parallel-developed around the central André-Oort conjecture. These two themes can be placed in a common frame--the Zilber-Pink conjecture. This volume is an introduction to these problems and to the various techniques used: geometry, height theory, reductive groups and Hodge theory, Shimura varieties, and model theory via the notion of o-minimal structure."--Publisher.
Author | : Enrico Bombieri |
Publisher | : Cambridge University Press |
Total Pages | : 676 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9780521712293 |
Download Heights in Diophantine Geometry Book in PDF, ePub and Kindle
This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.