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arXiv · 2411.01869

Mixed modular perverse sheaves on affine flag varieties and Koszul duality

Simon Riche
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Abstract

Under some technical assumptions, and building on joint work with Bezrukavnikov, we prove a multiplicity formula for indecomposable tilting perverse sheaves on affine flag varieties, with coefficients in a field of characteristic $p$, in terms of $p$-Kazhdan--Lusztig polynomials. Under the same assumptions, we also explain the construction of a "degrading functor" relating mixed modular perverse sheaves (as defined in joint work with Achar) on such varieties to ordinary perverse sheaves.

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Simon Riche. 2024-11-04. Mixed modular perverse sheaves on affine flag varieties and Koszul duality. https://arxiv.org/abs/2411.01869

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