Connections on conformal blocks
Name
767908297-MIT.pdf
Description
Full printable version
Size
3.35 MB
Format
Adobe PDF
Checksum (MD5)
bee56926211e1c6e32299070d53d8964
Author(s)
Rozenblyum, Nikita
Advisor(s)
Jacob Lurie.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 66-67).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
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