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Sen operators and Lie algebras arising from Galois representations over p-adic varieties

By Tongmu He

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-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 of the chart. When the representation comes from a $Q_{p}$-representation of a $p$-adic Lie group quotient of the fundamental group, we describe its Lie algebra action in terms of the Sen operators, which is a generalization of a result of Sen-Ohkubo. These Sen operators can be extended continuously to certain infinite-dimensional representations. As an application, we prove that the geometric Sen operators annihilate locally analytic vectors, generalizing a result of Pan.

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Citation data

  • DOI 10.24350/CIRM.V.19927803
  • Cite this video He Tongmu (6/3/22). Sen operators and Lie algebras arising from Galois representations over p-adic varieties. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19927803
  • URL https://dx.doi.org/10.24350/CIRM.V.19927803


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