G-equivariance of formal models of flag varieties

Abstract : Let G be a split connected reductive group scheme over the ring of integers of a finite extension L of Q_p and \lambda an algebraic character of a split maximal torus T. Let us also consider X^{rig} the rigid analytic flag variety of G. In the first part of this paper, we introduce a family of \lambda-twisted differential operators on a formal model Y of X^{rig}. 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(L)-equivariant arithmetic D(\lambda)-modules over the family of formal models of the rigid flag variety X^{rig}. We show that if /lambda is such that \lambda+\rho is dominant and regular (\rho being the Weyl character), then the preceding category is anti-equivalent to the category of admissible locally analytic-representations, with central character \lambda. In particular, we generalize the results in [25] for algebraic characters.
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Contributor : Andrés Sarrazola Alzate <>
Submitted on : Wednesday, October 16, 2019 - 10:12:45 AM
Last modification on : Saturday, October 19, 2019 - 1:22:42 AM

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Andrés Sarrazola Alzate. G-equivariance of formal models of flag varieties. 2019. ⟨hal-02317501⟩

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