Oriented cohomology sheaves on double moment graphs

TL;DR

This paper extends sheaf theory on moment graphs to arbitrary oriented equivariant cohomology, introducing double moment graph sheaves to analyze the equivariant cohomology of product flag varieties, especially for type A.

Contribution

It generalizes sheaf theory on moment graphs to oriented cohomology and introduces double moment graph sheaves for product varieties, linking to equivariant motives.

Findings

Double structure h-sheaves describe equivariant cohomology of product flag varieties.

Global sections of these sheaves relate to endomorphism rings of equivariant motives.

Extension to algebraic cobordism broadens applicability of moment graph techniques.

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.