Oriented cohomology sheaves on double moment graphs

Abstract

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. Contents 1. Introduction 1 2. Preliminaries 3 3. Equivariant oriented cohomology of the products 7 4. Double moment graphs 11 5. Closed double moment graphs 15 6. Global sections of structure sheaves 20 7. Correspondence product and equivariant motives 25 8. Appendix (type B) 28 References 36