Memoirs of the American Mathematical Society· 2026Q1
Free-Monodromic Mixed Tilting Sheaves on Flag Varieties
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- Q1SCImago
- 2026year
Short summary
A new monoidal category of "free-monodromic" tilting perverse sheaves on flag varieties is constructed, mirroring characteristic 0 properties.
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Key points
- Introduces a monoidal category of free-monodromic tilting perverse sheaves.
- Operates within the mixed modular derived category framework.
- Mirrors properties of characteristic 0 tilting perverse sheaves.
- Serves as a key ingredient for modular Koszul duality.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper we propose a construction of a monoidal category of “free-monodromic” tilting perverse sheaves on (Kac–Moody) flag varieties in the setting of the “mixed modular derived category” introduced by the first and third authors. This category shares most of the properties of their counterpart in characteristic 0 0 , defined by Bezrukavnikov–Yun using certain pro-objects in triangulated categories. This construction is the main new ingredient in the construction of a “modular Koszul duality” equivalence for constructible sheaves on flag varieties, see [J. Amer. Math. Soc. 32 (2019), no. 1, 261–310, DOI 10.1090/jams/905. MR 3868004 ].
The authors' abstract, as published at the source. Memoirs of the American Mathematical Society, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics