An example of the Langlands correspondence for irregular rank two connections on P^1

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.

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

References in corpus (4)

• Good moduli spaces for Artin stacks
• Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics
• Algebraic and hamiltonian approaches to isostokes deformations
• Moduli Spaces of Semistable Sheaves on Singular Genus One Curves

Cited by in corpus (2)

• Normal forms for rank two linear irregular differential equations and moduli spaces
• Geometric Langlands for hypergeometric sheaves