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Oriented cohomology sheaves on double moment graphs. (English) Zbl 1428.14027

Summary: In the present paper we extend the theory of sheaves on moment graphs due to Braden-MacPherson and Fiebig to the context of an arbitrary oriented equivariant cohomology h (e.g. to algebraic cobordism). We introduce and investigate structure h-sheaves on double moment graphs to describe equivariant oriented cohomology of products of flag varieties. We show that in the case of a total flag variety \(X\) of Dynkin type \(A\) the space of global sections of the double structure h-sheaf also describes the endomorphism ring of the equivariant h-motive of \(X\).

MSC:

14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14M15 Grassmannians, Schubert varieties, flag manifolds
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