Monday, March 7, 2022
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All day |
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4:00pm |
03/07/2022 - 4:30pm For a class of quotient stacks V/G for G a reductive group and V a symmetric G-representation, we propose a definition of the intersection K-theory of the quotient V//G, which is a Q-vector space denoted IK(V//G). There is a Chern character from IK(V//G) to intersection cohomology IH(V//G) and IK(V//G) satisfies Kirwan surjectivity. We construct IK(V//G) as a direct summand of the Grothendieck group (tensor with Q) of a noncommutative resolution of singularities of V//G constructed by Spenko-Van den Bergh. We explain extensions of some of these results for stacks with good moduli spaces. We discuss an application of this construction to a PBW-type theorem for (Kontsevich-Soibelman) K-theoretic Hall algebras of quivers with potential. Location:
Zoom
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