English

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