2015/11/05 by Laurent Berger, Peter Schneider, Berger, Laurent +3
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Pharmacological Effects of Natural Compounds #math.NT #msc:11F #msc:11S #msc:14G #msc:22E #msc:46S
paper · pdf · doi:10.48550/arxiv.1511.01819
69 pages
arxiv created 2015/11/05 · arxiv updated 2015/11/06
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 our 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, we work over a character variety, that parameterizes the locally L-analytic characters on oL. We study (φ,Γ)-modules in this setting, and relate some of them to what was known previously.