arithmetic duality theorems

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1、ArithmeticDualityTheoremsSecondEditionJ.S.MilneCopyright
c2004,2006J.S.Milne.TheelectronicversionofthisworkislicensedunderaCreativeCommonsLi-cense:http://creativecommons.org/licenses/by-nc-nd/2.5/Briefly,youarefreetocopytheelectronicversionoftheworkfornoncommercialpurposesundercertai

2、nconditions(seethelinkforaprecisestatement).Singlepapercopiesfornoncommercialpersonalusemaybemadewithoutex-plicitpermissionfromthecopyrightholder.Allotherrightsreserved.FirsteditionpublishedbyAcademicPress1986.Apaperbackversionofthisworkisavailablefrombooksellersworldwideandfromthep

3、ublisher:BookSurge,LLC,www.booksurge.com,1-866-308-6235,orders@booksurge.comBibTeXinformation@book{milne2006,author={J.S.Milne},title={ArithmeticDualityTheorems},year={2006},publisher={BookSurge,LLC},edition={Second},pages={viii+339},isbn={1-4196-4274-X}}QA247.M554ContentsContentsii

4、iIGaloisCohomology10Preliminaries............................21Dualityrelativetoaclassformation................172Localfields.............................263Abelianvarietiesoverlocalfields..................404Globalfields.............................485GlobalEuler-Poincar´echaracterist

5、ics................666Abelianvarietiesoverglobalfields.................727AnapplicationtotheconjectureofBirchandSwinnerton-Dyer..938Abelianclassfieldtheory......................1019Otherapplications..........................116AppendixA:Classfieldtheoryforfunctionfields............126II

6、EtaleCohomology1390Preliminaries............................1391Localresults.............................1482Globalresults:preliminarycalculations..............1633Globalresults:themaintheorem..................1764Globalresults:complements....................1885Globalresults:abelia

7、nschemes...................1976Globalresults:singularschemes..................2057Globalresults:higherdimensions.................208IIIFlatCohomology2170Preliminaries............................2181Localresults:mixedcharacteristic,finitegroupschemes.....2322Localresults:mixedcharacte

8、ristic,abelianvarie