CSAM101Central Simple Algebras and Galois Cohomology Gille Szamuely-Philippe Gille, Tamás Szamuely

《CSAM101Central Simple Algebras and Galois Cohomology Gille Szamuely-Philippe Gille, Tamás Szamuely》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ThispageintentionallyleftblankCentralSimpleAlgebrasandGaloisCohomologyThisbookisthefirstcomprehensive,modernintroductiontothetheoryofcentralsimplealgebrasoverarbitraryfields.Startingfromthebasics,itreachessuchadvancedresultsastheMerkurjev–Suslintheorem.Thistheoremisboththeculminati

2、onofworkinitiatedbyBrauer,Noether,HasseandAlbertinthe1930sandthestartingpointofmotiviccohomologytheory,adomainattheforefrontofcurrentresearchinalgebraicgeometryandK-theoryandthesettingofrecentspectacularworkbyVoevodsky,Suslin,Rostandothers.Assumingonlyasolidbackgroundinalgebra,bu

3、tnohomologicalalgebra,thebookcoversthebasictheoryofcentralsimplealgebras,methodsofGaloisdescentandGaloiscohomology,Severi–Brauervarieties,residuemapsand,finally,MilnorK-theoryandK-cohomology.Anumberofnoteworthyadditionaltopicsarealsocovered.Thelastchapterroundsoffthetheorybypresen

4、tingtheresultsinpositivecharacteristic,includingthetheoremofBloch–Gabber–Kato.Thebookissuitableasatextbookforgraduatestudentsandasareferenceforresearchersworkinginalgebra,algebraicgeometryorK-theory.philippegilleisCharg´edeRecherches,CNRS,Universit´edeParis-Sud,Orsay.tama´sszamue

5、lyisSeniorResearchFellow,Alfr´edR´enyiInstituteofMathematics,HungarianAcademyofSciences,Budapest.CAMBRIDGESTUDIESINADVANCEDMATHEMATICS101EDITORIALBOARDB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,´P.SARNAK,B.SIMON,B.TOTAROCENTRALSIMPLEALGEBRASANDGALOISCOHOMOLOGYCAMBRIDGESTUDIESINADVANCED

6、MATHEMATICSEditorialBoard:B.Bollob´as,W.Fulton,A.Katok,F.Kirwan,P.Sarnak,B.Simon,B.TotaroAlreadypublished35J.Palis&F.TakensHyperbolicity,stabilityandchaosathomoclinicbifurcations37Y.MeyerWaveletsandoperatorsI38C.WeibelAnintroductiontohomologicalalgebra39W.Bruns&J.HerzogCohen-Maca

7、ulayrings40V.SnaithExplicitBrauerinduction41G.LaumonCohomologyofDrinfeldmodularvarietiesI42E.B.DaviesSpectraltheoryanddifferentialoperators43J.Diestel,H.Jarchow,&A.TongeAbsolutelysummingoperators44P.MattilaGeometryofsetsandmeasuresinEuclideanspaces45R.PinskyPositiveharmonicfuncti

8、onsanddiffusion46G.TenenbaumIntroduction