Connections on conformal blocks

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2011

Author dc:creator

• Rozenblyum, Nikita

Advisor dc:contributor.advisor

• Jacob Lurie.

• Mathematics.

Statement 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/67813

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/67813