01638nam a22002657a 4500 55773 55773 20191021142004.0 191021b ||||| |||| 00| 0 eng d 9781470454753 516.35 POO Poonen, Bjorn Rational Points on Varieties / Bjorn Poonen rovidence, Rhode Island : American Mathematical Society, 2017 xv, 337 pages : illustrations ; 27 cm. Graduate studies in mathematics, v. 186. 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. 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. Mathematics Geometry Rational points Geometry Algebraic varieties. Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points. Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Varieties over global fields. Poonen, Bjorn MDL 0 0 ddc 0 0 MDL SNUL 2019-10-21 0 516.35 POO M042 2019-10-21 00:00:00 2019-10-21 MDL