Riemann–Hilbert for tame complex parahoric connections

By P. Boalch. 2010

59 citations recorded by the source corpus.

A local Riemann–Hilbert correspondence for tame meromorphic connections on a curve compatible with a parahoric level structure will be established. Special cases include logarithmic connections on G-bundles and on parabolic G-bundles. The corresponding Betti data involves pairs (M, P) consisting of the local monodromy M ∈ G and a (weighted) parabolic subgroup P ⊂ G such that M ∈ P, as in the multiplicative Brieskorn–Grothendieck–Springer resolution (extended to the parabolic case). The natural quasi-Hamiltonian structures that arise on such spaces of enriched monodromy data will also be constructed.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a6ca87f03ca684e243369f0ddd1a82815017d5f4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Carlos Simpson
2. P. Boalch
3. T. Mochizuki
4. Daisuke Yamakawa
5. Dan Xie

In Mathematical Physics

1. Carlos Simpson
2. P. Boalch
3. T. Mochizuki
4. Daisuke Yamakawa
5. Dan Xie

Citations in the corpus

• Local Systems on Proper Algebraic V -manifolds (2010, background): “The analogue of parabolic structures for principal G-bundles is not completely straightforward: one needs to introduce the notion of parahoric structure, and this is the subject of current ongoing research by several authors [17] [6].”
• Geometry and braiding of Stokes data; Fission and wild character varieties (2011, methodology): “B] (weighted conjugacy classes) to obtain spaces of Betti data (filtered Stokes representations) corresponding to meromorphic connections with unramified formal types on parahoric bundles, as in [59], [69], [19] in the tame case.”