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SUMMARY:Kirill Zainoulline (University of Ottawa)
DTSTART:20210630T181500Z
DTEND:20210630T190500Z
DTSTAMP:20260413T062335Z
UID:zoomnovy/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zoomnovy/11/
 ">Localized cohomological operations</a>\nby Kirill Zainoulline (Universit
 y of Ottawa) as part of Algebraic groups and algebraic geometry: in honor 
 of Zinovy Reichstein's 60th birthday\n\n\nAbstract\nCohomological operatio
 ns in algebraic oriented cohomology theories of Levine-Morel (Steenrod ope
 rations in Chow groups\; Adams operations in connective K-theory of Cai-Me
 rkurjev\; Landweber-Novikov operations and Vishik symmetric operations in 
 algebraic cobordism) provide a useful tool to study algebraic cycles on pr
 ojective homogeneous varieties G/P.\nIn the talk\, I will show how to exte
 nd these operations to a T-equivariant setup\, where T is a split maximal 
 torus of a semisimple linear algebraic group G over a field of characteris
 tic zero. More generally\, I will show how to extend it to structure algeb
 ras of moment graphs (rings of global sections of structure sheaves on mom
 ent graphs).\nI will explain a uniform algorithm that computes the usual (
 non-equivariant) operations for G/Ps using such extended (localized) opera
 tions and equivariant Schubert calculus techniques. This generalizes the a
 pproach suggested by Garibaldi-Petrov-Semenov for Steenrod operations. Exa
 mples include Adams operations\, L.-N. operations and Vishik's Mod-p opera
 tions.\n
LOCATION:https://researchseminars.org/talk/zoomnovy/11/
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