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

Download or read book Rigid Character Groups, Lubin-Tate Theory, and (phi, Gamma)--modules written by Laurent Berger and published by . This book was released on 2020 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The construction of the p-adic local Langlands correspondence for \mathrm{GL}_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 \mathrm{GL}_{2}(L), where L is a finite extension of \mathbf{Q}_p, it seems necessary to have at our disposal a theory of Lubin-Tate (\varphi ,\Gamma )-modules. Such a generalization has been carr.