K-Motives and Koszul Duality

2019/09/24 by Eberhardt, Jens Niklas · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1909.11151

Abstract

We construct an ungraded version of Beilinson-Ginzburg-Soergel's Koszul duality for Langlands dual flag varieties, inspired by Beilinson's construction of rational motivic cohomology in terms of K-theory. For this, we introduce and study categories DK_S(X) of S-constructible K-motivic sheaves on varieties X with an affine stratification S. We show that there is a natural and geometric functor, called Beilinson realisation, from S-constructible mixed sheaves D^mix_S(X) to DK_S(X). We then show that Koszul duality intertwines the Betti realisation and Beilinson realisation functors and descends to an equivalence of constructible sheaves and constructible K-motivic sheaves on Langlands dual flag varieties.

Cited by

• The Parabolic K-motivic Hecke Category
• Equivariant localizing invariants of simple varieties

Related

• Universal Koszul Duality for Kac-Moody Groups
• Koszul duality for toric varieties
• K-motives of algebraic varieties
• Koszul duality and semisimplicity of Frobenius
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