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

Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules
Author :
Publisher : American Mathematical Soc.
Total Pages : 92
Release :
ISBN-10 : 9781470440732
ISBN-13 : 1470440733
Rating : 4/5 (733 Downloads)

Book Synopsis Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by : Laurent Berger

Download or read book Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules written by Laurent Berger and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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