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

Modular Forms and Galois Cohomology (Cambridge Studies in Advanced Mathematics)
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作者: 著
出版社: Cambridge University Press
2008-08
版次: 1
ISBN: 9780521072083
定价: 612.20
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 356页
正文语种: 英语
分类: 外文古旧书>英文书>工程技术
  • Thisbookprovidesacomprehensiveaccountofakey(andperhapsthemostimportant)theoryuponwhichtheTaylor–WilesproofofFermat'slasttheoremisbased.Thebookbeginswithanoverviewofthetheoryofautomorphicformsonlinearalgebraicgroupsandthencoversthebasictheoryandresultsonellipticmodularforms,includingasubstantialsimplificationoftheTaylor–WilesproofbyFujiwaraandDiamond.Itcontainsadetailedexpositionoftherepresentationtheoryofprofinitegroups(includingdeformationtheory),aswellastheEulercharacteristicformulasofGaloiscohomologygroups.Thefinalchapterpresentsaproofofanon-abelianclassnumberformulaandincludesseveralnewresultsfromtheauthor.Thebookwillbeofinteresttograduatestudentsandresearchersinnumbertheory(includingalgebraicandanalyticnumbertheorists)andarithmeticalgebraicgeometry. Preface

    1. Overview of modular forms

    2. Representations of a group

    3. Representations and modular forms

    4. Galois cohomology

    5. Modular L-values and Selmer groups

    Bibliography

    Subject index

    List of statements

    List of symbols.
  • 内容简介:
    Thisbookprovidesacomprehensiveaccountofakey(andperhapsthemostimportant)theoryuponwhichtheTaylor–WilesproofofFermat'slasttheoremisbased.Thebookbeginswithanoverviewofthetheoryofautomorphicformsonlinearalgebraicgroupsandthencoversthebasictheoryandresultsonellipticmodularforms,includingasubstantialsimplificationoftheTaylor–WilesproofbyFujiwaraandDiamond.Itcontainsadetailedexpositionoftherepresentationtheoryofprofinitegroups(includingdeformationtheory),aswellastheEulercharacteristicformulasofGaloiscohomologygroups.Thefinalchapterpresentsaproofofanon-abelianclassnumberformulaandincludesseveralnewresultsfromtheauthor.Thebookwillbeofinteresttograduatestudentsandresearchersinnumbertheory(includingalgebraicandanalyticnumbertheorists)andarithmeticalgebraicgeometry.
  • 目录:
    Preface

    1. Overview of modular forms

    2. Representations of a group

    3. Representations and modular forms

    4. Galois cohomology

    5. Modular L-values and Selmer groups

    Bibliography

    Subject index

    List of statements

    List of symbols.
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