Share

Rational Points on Varieties

2017-12-13 Mathematics
Download Rational Points on Varieties PDF Online Free

Author :
Release : 2017-12-13
Genre : Mathematics
Kind : eBook
Book Rating : 732/5 ( reviews)

GET EBOOK


Book Synopsis Rational Points on Varieties by : Bjorn Poonen

Download or read book Rational Points on Varieties written by Bjorn Poonen. This book was released on 2017-12-13. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rational Points on Varieties

2023-08-10 Mathematics
Download Rational Points on Varieties PDF Online Free

Author :
Release : 2023-08-10
Genre : Mathematics
Kind : eBook
Book Rating : 581/5 ( reviews)

GET EBOOK


Book Synopsis Rational Points on Varieties by : Bjorn Poonen

Download or read book Rational Points on Varieties written by Bjorn Poonen. This book was released on 2023-08-10. Available in PDF, EPUB and Kindle. Book excerpt: 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

Rational Points on Algebraic Varieties

2012-12-06 Mathematics
Download Rational Points on Algebraic Varieties PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 684/5 ( reviews)

GET EBOOK


Book Synopsis Rational Points on Algebraic Varieties by : Emmanuel Peyre

Download or read book Rational Points on Algebraic Varieties written by Emmanuel Peyre. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Higher Dimensional Varieties and Rational Points

2013-12-11 Mathematics
Download Higher Dimensional Varieties and Rational Points PDF Online Free

Author :
Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 230/5 ( reviews)

GET EBOOK


Book Synopsis Higher Dimensional Varieties and Rational Points by : Károly Jr. Böröczky

Download or read book Higher Dimensional Varieties and Rational Points written by Károly Jr. Böröczky. This book was released on 2013-12-11. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Arithmetic of Higher-Dimensional Algebraic Varieties

2012-12-06 Mathematics
Download Arithmetic of Higher-Dimensional Algebraic Varieties PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 701/5 ( reviews)

GET EBOOK


Book Synopsis Arithmetic of Higher-Dimensional Algebraic Varieties by : Bjorn Poonen

Download or read book Arithmetic of Higher-Dimensional Algebraic Varieties written by Bjorn Poonen. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...