-equivariance of formal models of flag varieties
Andrés Sarrazola Alzate
University of Padova, Italy
![$G$-equivariance of formal models of flag varieties cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rsmup-volume-150.png&w=3840&q=90)
Abstract
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.
Cite this article
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