Revista de la
Unión Matemática Argentina
Mixed modular perverse sheaves on affine flag varieties and Koszul duality
Simon Riche

Volume 69, no. 1 (2026), pp. 373–410    

Published online (final version): April 20, 2026

https://doi.org/10.33044/revuma.5035

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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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