-equivariance of formal models of flag varieties

  • Andrés Sarrazola Alzate

    University of Padova, Italy
$G$-equivariance of formal models of flag varieties cover
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Let be a split connected reductive group scheme over the ring of integers of a finite extension and an algebraic character of a split maximal torus . Let us also consider the rigid analytic flag variety of and . In the first part of this paper, we introduce a family of -twisted differential operators on a formal model of . We compute their global sections and we prove coherence together with several cohomological properties. In the second part, we define the category of coadmissible -equivariant arithmetic -modules over the family of formal models of the rigid flag variety . We show that if is such that is dominant and regular ( being the Weyl character), then the preceding category is anti-equivalent to the category of admissible locally analytic -representations, with central character . In particular, we generalize the main results from a paper by Huyghe, Patel, Schmidt and Strauch (2019) for algebraic characters.

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Andrés Sarrazola Alzate, -equivariance of formal models of flag varieties. Rend. Sem. Mat. Univ. Padova 150 (2023), pp. 1–79

DOI 10.4171/RSMUP/104