Rational Points on Varieties

Thisbookismotivatedbytheproblemofdeterminingthesetofrationalpointsonavariety,butitstruegoalistoequipreaderswithabroadrangeoftoolsessentialforcurrentresearchinalgebraicgeometryandnumbertheory.Thebookisunconventionalinthatitprovidesconciseaccountsofmanytopicsinsteadofacomprehensiveaccountofjustone—thisisintentionallydesignedtobringreadersuptospeedrapidly.AmongthetopicsincludedareBrauergroups,faithfullyflatdescent,algebraicgroups,torsors,étaleandfppfcohomology,theWeilconjectures,andtheBrauer-Maninanddescentobstructions.Afinalchapterappliesallthesetostudythearithmeticofsurfaces.Thedown-to-earthexplanationsandtheover100exercisesmakethebooksuitableforuseasagraduate-leveltextbook,butevenexpertswillappreciatehavingasinglesourcecoveringmanyaspectsofgeometryoveranunrestrictedgroundfieldandcontainingsomematerialthatcannotbefoundelsewhere.