{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/67813"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/67813","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Connections on conformal blocks","abstract":"For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.e. quasi-coherent sheaves with a flat connection. This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.","abstract_html":"For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points of X. We show that sheaves which are, in a certain sense, equivariant with respect to infinitesimal Hecke functors are exactly D-modules, i.e. quasi-coherent sheaves with a flat connection. This gives a description of flat connections on a quasi-coherent sheaf on Bung which is local on the Ran space.","abstract_has_math":false,"creators":["Rozenblyum, Nikita"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Jacob Lurie."],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-22T22:20:48Z","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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