The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.
The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory.
The notes by Gebhard Bockle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and...
The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geom...
The construction of the $p$-adic local Langlands correspondence for $mathrm_2(mathbf_p)$ uses in an essential way Fontaine's theory of cyclotomic $(varphi ,Gamma )$-modules. Here cyclotomic means that $Gamma = mathrm (mathbf_p(mu_{p^infty})/mathbf_p)$ is the Galois group of the cyclotomic extension of $mathbf Q_p$. In order to generalize the $p$-adic local Langlands correspondence to $mathrm_(L)$, where $L$ is a finite extension of $mathbf_p$, it seems necessary to have at our disposal a theory of Lubin-Tate $(varphi ,Gamma )$-modules. Such a generalization has...
The construction of the $p$-adic local Langlands correspondence for $mathrm_2(mathbf_p)$ uses in an essential way Fontaine's theory of cyclotom...
