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 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 of Dynkin type the space of global sections of the double structure h-sheaf also describes the endomorphism ring of the equivariant h-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