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Rational points on varieties

Author: Bjorn Poonen
Publisher: Providence, Rhode Island : American Mathematical Society, [2017]
Series: Graduate studies in mathematics, v. 186.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2017022803
(OCoLC)987437380
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bjorn Poonen
ISBN: 9781470443153 1470443155
OCLC Number: 1016626650
Description: 1 online resource (1 volume)
Contents: Preface --
Fields --
Varieties over arbitrary fields --
Properties of morphisms --
Faithfully flat descent --
Algebraic groups --
Êtale and fppf cohomology --
The Weil conjectures --
Cohomological obstructions to rational points --
Surfaces --
Appendix A. Universes --
Appendix B. Other kinds of fields --
Appendix C. Properties under base extension.
Series Title: Graduate studies in mathematics, v. 186.
Responsibility: Bjorn Poonen.

Abstract:

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  Read more...

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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 Read more...

 
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