Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules

Released on by Laurent Berger
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  • Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules Book Detail

  • Author : Laurent Berger
  • Release Date : 2020-04-03
  • Publisher : American Mathematical Soc.
  • Genre : Education
  • Pages : 75
  • ISBN 13 : 1470440733
  • File Size : 15,15 MB
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Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by Laurent Berger PDF Summary

Book Description: The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.

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