Integral Points On Algebraic Varieties
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Integral Points On Algebraic Varieties
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Author : Pietro Corvaja
language : en
Publisher: Springer
Release Date : 2016-11-23
Integral Points On Algebraic Varieties written by Pietro Corvaja and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Mathematics categories.
This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.
Rational Points On Algebraic Varieties
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Author : Emmanuel Peyre
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Rational Points On Algebraic Varieties written by Emmanuel Peyre and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.
Rational Points On Varieties
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Author : Bjorn Poonen
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-10
Rational Points On Varieties written by Bjorn Poonen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-10 with Mathematics categories.
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University
Arithmetic Of Higher Dimensional Algebraic Varieties
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Author : Bjorn Poonen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetic Of Higher Dimensional Algebraic Varieties written by Bjorn Poonen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.
Birational Geometry Rational Curves And Arithmetic
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Author : Fedor Bogomolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-17
Birational Geometry Rational Curves And Arithmetic written by Fedor Bogomolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-17 with Mathematics categories.
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Ample Subvarieties Of Algebraic Varieties
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Author : Robin Hartshorne
language : en
Publisher: Springer
Release Date : 2006-11-15
Ample Subvarieties Of Algebraic Varieties written by Robin Hartshorne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Rational Points Rational Curves And Entire Holomorphic Curves On Projective Varieties
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Author : Carlo Gasbarri
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-22
Rational Points Rational Curves And Entire Holomorphic Curves On Projective Varieties written by Carlo Gasbarri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic problems. Diophantine geometry categories.
This volume contains papers from the Short Thematic Program on Rational Points, Rational Curves, and Entire Holomorphic Curves and Algebraic Varieties, held from June 3-28, 2013, at the Centre de Recherches Mathématiques, Université de Montréal, Québec, Canada. The program was dedicated to the study of subtle interconnections between geometric and arithmetic properties of higher-dimensional algebraic varieties. The main areas of the program were, among others, proving density of rational points in Zariski or analytic topology on special varieties, understanding global geometric properties of rationally connected varieties, as well as connections between geometry and algebraic dynamics exploring new geometric techniques in Diophantine approximation. This book is co-published with the Centre de Recherches Mathématiques.
Rational Points On Algebraic Varieties
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Author : Emmanuel Peyre
language : en
Publisher: Birkhauser
Release Date : 2001
Rational Points On Algebraic Varieties written by Emmanuel Peyre and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Algebraic Surfaces
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Author : Oscar Zariski
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-02-15
Algebraic Surfaces written by Oscar Zariski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-15 with Mathematics categories.
From the reviews: "The author's book [...] saw its first edition in 1935. [...] Now as before, the original text of the book is an excellent source for an interested reader to study the methods of classical algebraic geometry, and to find the great old results. [...] a timelessly beautiful pearl in the cultural heritage of mathematics as a whole." Zentralblatt MATH
Brauer Groups Tamagawa Measures And Rational Points On Algebraic Varieties
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Author : Jorg Jahnel
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-02
Brauer Groups Tamagawa Measures And Rational Points On Algebraic Varieties written by Jorg Jahnel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type--both in terms of when such points exist and, if they do, their quantitative density. The book consists of three parts. In the first part, the author discusses the concept of a height and formulates Manin's conjecture on the asymptotics of rational points on Fano varieties. The second part introduces the various versions of the Brauer group. The author explains why a Brauer class may serve as an obstruction to weak approximation or even to the Hasse principle. This part includes two sections devoted to explicit computations of the Brauer-Manin obstruction for particular types of cubic surfaces. The final part describes numerical experiments related to the Manin conjecture that were carried out by the author together with Andreas-Stephan Elsenhans. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area.