Devyatov, Rostislav; Lanini, Martina; Zainoulline, Kirill

Oriented Cohomology Sheaves on Double Moment Graphs

Doc. Math. 24, 563-608 (2019)
DOI: 10.25537/dm.2019v24.563-608
Communicated by Nikita Karpenko

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 \texttt{h} (e.g. to algebraic cobordism). We introduce and investigate structure \texttt{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 \texttt{h}-sheaf also describes the endomorphism ring of the equivariant \texttt{h}-motive of \(X\).

Mathematics Subject Classification

14F05, 14F43, 14M15

Keywords/Phrases

moment graph, equivariant cohomology, motive, projective homogeneous space

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Affiliation

Devyatov, Rostislav
Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, T6G 2G1, Canada
Lanini, Martina
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Rome, Italy
Zainoulline, Kirill
Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, ON, K1N 6N5, Canad

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