Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma)--modules

Released on by Laurent Berger
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  • Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma)--modules Book Detail

  • Author : Laurent Berger
  • Release Date : 2020
  • Publisher :
  • Genre : Class field theory
  • Pages : 79
  • ISBN 13 : 9781470456580
  • File Size : 18,18 MB
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Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma)--modules by Laurent Berger PDF Summary

Book Description: The construction of the p-adic local Langlands correspondence for \mathrm{GL}_2(\mathbf{Q}_p) uses in an essential way Fontaine's theory of cyclotomic (\varphi ,\Gamma )-modules. Here cyclotomic means that \Gamma = \mathrm {Gal}(\mathbf{Q}_p(\mu_{p^\infty})/\mathbf{Q}_p) is the Galois group of the cyclotomic extension of \mathbf Q_p. In order to generalize the p-adic local Langlands correspondence to \mathrm{GL}_{2}(L), where L is a finite extension of \mathbf{Q}_p, it seems necessary to have at our disposal a theory of Lubin-Tate (\varphi ,\Gamma )-modules. Such a generalization has been carr.

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The $K$-book

The $K$-book

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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vec