An example of the Langlands correspondence for irregular rank two connections on P^1
Algebraic Geometry
2012-05-03 v3
Abstract
Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived category of modules over a TDO ring on certain non-separated curve. We identify this curve with the coarse moduli space of some parabolic bundles on P^1. Then our equivalence becomes an example of the categorical Langlands correspondence.
Keywords
Cite
@article{arxiv.1003.6112,
title = {An example of the Langlands correspondence for irregular rank two connections on P^1},
author = {Dmitry Arinkin and Roman Fedorov},
journal= {arXiv preprint arXiv:1003.6112},
year = {2012}
}
Comments
Section 5 was shortened by referring to results of Hernandez Ruiperez et al. The reader might want to look at the previous (2nd) version for a more self-contained exposition. Other minor changes