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 nonintegral slope. Finally, we construct a moduli space of meromorphic connections on the projective line with specified formal type at the singular points. © 2012 The Author(s).
Publication Source (Journal or Book title)
International Mathematics Research Notices
Bremer, C., & Sage, D. (2013). Moduli spaces of irregular singular connections. International Mathematics Research Notices, 2013 (8), 1800-1872. https://doi.org/10.1093/imrn/rns103