01741nam a22002777a 4500999001700000005001700017008004100034020001800075082001500093100001800108245004900126260006900175300004700244490004500291505035800336520036300694650001601057650001301073650002901086650002501115650008801140650010701228700001801335942000801353952010201361 c55773d5577320191021142004.0191021b ||||| |||| 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 cMDL 00102ddc4070aMDLbSNULd2019-10-21l0o516.35 POOpM042r2019-10-21 00:00:00w2019-10-21yMDL