Equivariant deformations of the affine multicone over a flag variety

The affine flag variety

On GKM Description of the Equivariant Cohomology of Affine Flag Varieties and Affine Springer Fibers

For a projective variety endowed with a torus action, the equivariant cohomology is determined by the fixed points of codimension 1 subtori. Especially, when the fixed points of the torus are finite and fixed varieties under the action of codimension 1 subtori have dimension less than or equal to 2, equivariant cohomology can be described by discrete conditions on the pair of fixed points via G...

Equivariant K-theory of Affine Flag Manifolds and Affine Grothendieck Polynomials

We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial, which we call the affine Grothendieck polynomial.

Flag Variety

1.1. QCoh on a stack. We know that QCoh forms a stack, i.e., sheaf of groupoids, over Schfpqc(S) for any scheme S. Thus if we have an fpqc sheaf of groupoids X over S, we can define QCoh(X ) as maps of sheaves X → QCoh on Schfpqc(S). By 2-Yoneda, this definition agrees with the usual notion of quasicoherent sheaves if X is a scheme. For various other (usually equivalent) definitions in the case...

Equivariant Sheaves on Flag Varieties

We show that the Borel-equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of dg modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves. This proves a conjecture of Soergel and Lunts in the case of flag varieties.