2026-09-19T11:38:12Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/678132022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Jacob Lurie.
Rozenblyum, Nikita
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2011-12-19T19:00:52Z
2011-12-19T19:00:52Z
2011
2011
http://hdl.handle.net/1721.1/67813
767908297
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 66-67).
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.
by Nikita Rozenblyum.
Ph.D.
67 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Connections on conformal blocks
Thesis
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Publication
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