Modular Forms and Galois Cohomology (Cambridge Studies in Advanced Mathematics)

Thisbookprovidesacomprehensiveaccountofakey(andperhapsthemostimportant)theoryuponwhichtheTaylor–WilesproofofFermat'slasttheoremisbased.Thebookbeginswithanoverviewofthetheoryofautomorphicformsonlinearalgebraicgroupsandthencoversthebasictheoryandresultsonellipticmodularforms,includingasubstantialsimplificationoftheTaylor–WilesproofbyFujiwaraandDiamond.Itcontainsadetailedexpositionoftherepresentationtheoryofprofinitegroups(includingdeformationtheory),aswellastheEulercharacteristicformulasofGaloiscohomologygroups.Thefinalchapterpresentsaproofofanon-abelianclassnumberformulaandincludesseveralnewresultsfromtheauthor.Thebookwillbeofinteresttograduatestudentsandresearchersinnumbertheory(includingalgebraicandanalyticnumbertheorists)andarithmeticalgebraicgeometry.