01578nam a22002417a 450000500170000000800410001702000180005808200150007610000180009124500490010926000690015830000470022749000450027450503580031952003630067765000160104065000130105665000290106965000250109865000880112365001070121170000180131820191021142004.0191021b ||||| |||| 00| 0 eng d a9781470454753 a516.35 POO aPoonen, Bjorn aRational Points on Varietiesc/ Bjorn Poonen arovidence, Rhode Island b: American Mathematical Society,c2017 axv, 337 pages b: illustrations c; 27 cm. aGraduate studies in mathematics, v. 186. a 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. aThis 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. aMathematics aGeometry aRational points Geometry aAlgebraic varieties. aAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points. aNumber theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Varieties over global fields. aPoonen, Bjorn