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

Laurent BergerPeter SchneiderBingyong Xie

出版	American Mathematical Society, 1920
ISBN	14704565839781470456580
URL	http://books.google.com.hk/books?id=Hp76zQEACAAJ&hl=&source=gbs_api

註釋The construction of the p-adic local Langlands correspondence for mathrmGL}_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 mathrmGL}_{2}(L), where L is a finite extension of mathbfQ}_p, it seems necessary to have at our disposal a theory of Lubin-Tate ( varphi , Gamma )-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 ( varphi , Gamma )-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 o_L. They study ( varphi , Gamma )-modules in this setting and relate some of them to what was known previously.