2019/10/14 by Andrés Sarrazola Alzate, Alzate, Andrés Sarrazola
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1910.06439
Let \mathbbG be a split connected reductive group scheme over the ring of integers \mathfrako of a finite extension L|ℚp and λ∈ X(\mathbbT) an algebraic character of a split maximal torus \mathbbT⊆\mathbbG. Let us also consider Xrig the rigid analytic flag variety of \mathbbG and G=\mathbbG(L). In the first part of this paper, we introduce a family of λ-twisted differential operators on a formal model \mathfrakY of Xrig. We compute their global sections and we prove coherence together with several cohomological properties. In the second part, we define the category of coadmissible G-equivariant arithmetic D(λ)-modules over the family of formal models of the rigid flag variety Xrig. We show that if λ is such that λ+ ρ is dominant and regular (ρ being the Weyl character), then the preceding category is anti-equivalent to the category of admissible locally analytic G-representations, with central character λ. In particular, we generalize the results of Huyghe-Patel-Strauch-Schmidt for algebraic characters (cf. [25] in the text).