Moduli spaces of irregular singular connections

Details Moduli spaces of irregular singular connections Moduli spaces of irregular singular connections

2010-04-26

arxiv.org/abs/1004.4411v2

Mathematics

Algebraic Geometry

53 pages. A new section (Section 4.4) has been added making precise the relationship between formal types and isomorphism clas

Scientific paper

In the geometric version of the Langlands correspondence, irregular singular point connections play the role of Galois representations with wild ramification. In this paper, we develop a geometric theory of fundamental strata to study irregular singular connections on the projective line. Fundamental strata were originally used to classify cuspidal representations of the general linear group over a local field. In the geometric setting, fundamental strata play the role of the leading term of a connection. We introduce the concept of a regular stratum, which allows us to generalize the condition that a connection has regular semisimple leading term to connections with non-integer slope. Finally, we construct a symplectic moduli space of meromorphic connections on the projective line that contain a regular stratum at each singular point.

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