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Séminaire d'Arithmétique

École polytechnique  – Centre de Mathématiques Laurent Schwartz


14h00: Tongmu He (IHES)

"Sen Operators and Lie Algebras arising from Galois Representations over p-adic Varieties"


Résumé : Any finite-dimensional p-adic representation of the absolute Galois group of a p-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their construction to the fundamental group of a p-adic affine variety with a semi-stable chart, and prove that the module of Sen operators is canonically defined, independently of the choice fo the chart. When the representation comes from Qp-representation of the fundamental group, we relate the infinitesimal action of inertia subgroups with Sen operators, which is a generalization of a result of Sen and Ohkubo.