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 …

We initiate the study of KK‐theory Soergel bimodules, a global and KK‐theoretic version of
Soergel bimodules. We show that morphisms of KK‐theory Soergel bimodules can be …

For a variety with a Whitney stratification by affine spaces, we study categories of motivic
sheaves which are constant mixed Tate along the strata. We are particularly interested in …

We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic,
not only as Chow motives (due to Huybrechts), but also as Frobenius algebra objects …

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 …

In this paper, we construct four different theories of integration, two that are for Voevodsky
motives, one for mixed $\ell $-adic sheaves, and a fourth theory of integration for rational …

For any Kac-Moody group $ G $ with Borel $ B $, we give a monoidal equivalence between
the derived category of $ B $-equivariant mixed complexes on the flag variety $ G/B $ and (a …

The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge
structures or compactly supported $\ell $-adic cohomology. Zakharevich and\Campbell have …

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 …

We advance the understanding of K–theory of quadratic forms by computing the slices of the
motivic spectra representing hermitian K–groups and Witt groups. By an explicit computation …