Poonen, Bjorn creator Poonen, Bjorn text rovidence, Rhode Island : American Mathematical Society 2017 monographic eng

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xv, 337 pages : illustrations ; 27 cm. 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. 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. / Bjorn Poonen 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 516.35 POO 9781470454753 191021 20191021142004.0