Rigid Character Groups Lubin Tate Theory And Modules
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Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules
Author: Laurent Berger
language: en
Publisher: American Mathematical Soc.
Release Date: 2020-04-03
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.
Galois Representations and (Phi, Gamma)-Modules
Author: Peter Schneider
language: en
Publisher: Cambridge University Press
Release Date: 2017-04-20
A detailed and self-contained introduction to a key part of local number theory, ideal for graduate students and researchers.
Modern Trends in Algebra and Representation Theory
Author: David Jordan
language: en
Publisher: Cambridge University Press
Release Date: 2023-08-17
Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.