Duke Mathematical Journal

Modular perverse sheaves on flag varieties, II: Koszul duality and formality

Pramod N. Achar and Simon Riche

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Abstract

Building on the theory of parity sheaves due to Juteau, Mautner, and Williamson, we develop a formalism of “mixed modular perverse sheaves” for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a “Koszul-type” derived equivalence relating a given flag variety to the Langlands dual flag variety and (2) a formality theorem for the modular derived category of a flag variety (extending a previous result of Riche, Soergel, and Williamson).

Article information

Source
Duke Math. J., Volume 165, Number 1 (2016), 161-215.

Dates
Received: 3 February 2014
Revised: 20 December 2014
First available in Project Euclid: 19 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1445264289

Digital Object Identifier
doi:10.1215/00127094-3165541

Mathematical Reviews number (MathSciNet)
MR3450745

Zentralblatt MATH identifier
1375.14162

Subjects
Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 20G40: Linear algebraic groups over finite fields

Keywords
modular perverse sheaves Koszul duality flag varieties self-duality and formality

Citation

Achar, Pramod N.; Riche, Simon. Modular perverse sheaves on flag varieties, II: Koszul duality and formality. Duke Math. J. 165 (2016), no. 1, 161--215. doi:10.1215/00127094-3165541. https://projecteuclid.org/euclid.dmj/1445264289


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References

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