Rational points on varieties

Author(s)

• Poonen, Bjorn

Bibliographic Information

Rational points on varieties

Bjorn Poonen

（Graduate studies in mathematics, v. 186）

American Mathematical Society, c2017

Note

Includes bibliographical references (p. 311-329) and index

Description and Table of Contents

Description

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, etale 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.

Table of Contents

Fields Varieties over arbitrary fields Properties of morphisms Faithfully flat descent Algebraic groups Etale and fppf cohomology The Weil conjecture Cohomological obstructions to rational points Surfaces Universes Other kinds of fields Properties under base extension Bibliography Index

by "Nielsen BookData"

• NCID: BB25144817
• ISBN:
  • 9781470437732
• LCCN: 2017022803
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence
• Pages/Volumes: xv, 337 p.
• Size: 27 cm
• Classification:
  • DC23 : 516.35
• Subject Headings:
  • LCSH : Rational points (Geometry)
  • LCSH : Algebraic varieties
• Parent Bibliography ID:
  • BA20542214