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Euler Systems

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Title: Euler Systems
Description: One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
Authors: Karl Rubin
Resource Type: eBook.
Subjects: Algebraic number theory, p-adic numbers
Categories: MATHEMATICS / Number Theory, MATHEMATICS / Geometry / Algebraic
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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DbLabel: eBook Collection (EBSCOhost)
An: 818441
RelevancyScore: 1057
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PubType: eBook
PubTypeId: ebook
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  Data: Euler Systems
– Name: Abstract
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  Data: One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
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  Data: <searchLink fieldCode="DE" term="%22Algebraic+number+theory%22">Algebraic number theory</searchLink><br /><searchLink fieldCode="DE" term="%22p-adic+numbers%22">p-adic numbers</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.74
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Algebraic number theory
        Type: general
      – SubjectFull: p-adic numbers
        Type: general
    Titles:
      – TitleFull: Euler Systems
        Type: main
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          Name:
            NameFull: Karl Rubin
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            NameFull: Karl Rubin
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2014
            – D: 08
              M: 09
              Type: profile
              Y: 2014
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            – Type: isbn-print
              Value: 9780691050768
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              Value: 9780691050751
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              Value: 9781400865208
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            – Type: volume
              Value: 00147
          Titles:
            – TitleFull: Euler Systems
              Type: main
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