Oriented Cohomology Sheaves on Double Moment Graphs

  • Rostislav Devyatov

    Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, Ottawa, ON, K1N 6N5, Canada
  • Martina Lanini

    Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Rome, Italy
  • Kirill Zainoulline

    Department of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, T6G 2G1, Canada
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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 (e.g. to algebraic cobordism). We introduce and investigate structure -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 of Dynkin type the space of global sections of the double structure -sheaf also describes the endomorphism ring of the equivariant -motive of .

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Rostislav Devyatov, Martina Lanini, Kirill Zainoulline, Oriented Cohomology Sheaves on Double Moment Graphs. Doc. Math. 24 (2019), pp. 563–608

DOI 10.4171/DM/689