{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/67788"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/67788","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras","abstract":"In this thesis, we examine three different versions of \"categorification\" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is by certain categories of constructible sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche.","abstract_html":"In this thesis, we examine three different versions of "categorification" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is by certain categories of constructible sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche.","abstract_has_math":false,"creators":["Dodd, Christopher Stephen"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Roman Bezrukavnikov."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-22T22:21:19Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/67788"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. 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In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Roman Bezrukavnikov."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Dodd, Christopher Stephen"],"dc:date.accessioned":["2011-12-19T18:51:32Z"],"dc:date.available":["2011-12-19T18:51:32Z"],"dc:date.issued":["2011"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 97-100)."],"dc:description.abstract":["In this thesis, we examine three different versions of \"categorification\" of the affine Hecke algebra and its periodic module: the first is by equivariant coherent sheaves on the Grothendieck resolution (and related objects), the second is by certain classes on bimodules over polynomial rings, called Soergel bimodules, and the third is by certain categories of constructible sheaves on the affine flag manifold (for the Langlands dual group). We prove results relating all three of these categorifications, and use them to deduce nontrivial equivalences of categories. In addition, our main theorem allows us to deduce the existence of a strict braid group action on all of the categories involved; which strengthens a theorem of Bezrukavnikov-Riche."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/67788"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Equivariant coherent sheaves, Soergel bimodules, and categorification of affine Hecke algebras"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:19Z"}