Laboratoire Alexander Grothendieck, Institut des Hautes Études Scientifiques,
Morningside Center of Mathematics, Chinese Academy of Sciences,
Département des Sciences Mathématiques de l'Université de Tokyo

Ahmed Abbes (CNRS, IHÉS), Fabrice Orgogozo (CNRS, École polytechnique), Takeshi Saito (Université de Tokyo),
Atsushi Shiho (Université de Tokyo), Ye Tian (Morningside Center for Mathematics),
Takeshi Tsuji (Université de Tokyo), Weizhe Zheng (Morningside Center for Mathematics)

Mardi 29 mars 2016 de 11h45 à 12h45

T. Tsuji (University of Tokyo & IHÉS)

Notes on the local p-adic Simpson correspondence

The local p-adic Simpson correspondence by Faltings asserts that there is a natural equivalence of categories between small generalized representations and small Higgs modules for an affine semi-stable scheme over a complete discrete valuation ring of mixed characteristic with algebraically closed residue field. However, in the case of rational coefficients, the construction of the functor from the former to the latter, reducing to the theory for integral coefficients, does not seem to work as it is written, as pointed out by Ahmed Abbes. In this talk, I give an alternative argument based on a generalized Sen's theory for the semi-stable scheme and complete the local theory for rational coefficients.