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

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

2010-03-31

arxiv.org/abs/1003.6112v2

Mathematics

Algebraic Geometry

Introduction expanded; minor correctiouns throughout the text, including the statements of Corollary 6.8 and of Proposition 6.

Scientific paper

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.

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