135 citations · 176 across the 8 of their papers we have counts for
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Homological properties of representations of p-adic groups related to geometry of the group at infinity
Roman Bezrukavnikov
Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein'…
Cohomology of tilting modules over quantum groups and -structures on derived categories of coherent sheaves
Roman Bezrukavnikov
The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to…
Quantum Groups, the loop Grassmannian, and the Springer resolution
Sergey Arkhipov, Roman Bezrukavnikov, Victor Ginzburg
We establish equivalences of derived categories of the following 3 categories: (1) Principal block of representations of the quantum at a root of 1; (2) G-equivariant coherent shea…
Tilting exercises
A. Beilinson, R. Bezrukavnikov, I. Mirkovic
This is an application of the theory of tilting objects to the geometric setting of perverse sheaves. We show that this theory is a natural framework for Beilinson's gluing of perv…
Localization of modules for a semisimple Lie algebra in prime characteristic
Roman Bezrukavnikov, Ivan Mirković, Dmitriy Rumynin
We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic (where is the Coxet…
On tensor categories attached to cells in affine Weyl groups II
Roman Bezrukavnikov, Viktor Ostrik
George Lusztig conjectured that asymptotic affine Hecke algebra of a simply connected group can be explicitly described in terms of convolution algebras. Main Theorem of this note…