2021/07/14 by Phùng Hô Hái, João Pedro dos Santos, Hai, Phùng Hô +3 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2107.06474
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over C((x)) and \mathbb P1C\smallsetminus\0,∞\, where C is algebraically closed and of characteristic zero. It aims at reading the existing classification results as an equivalence between regular-singular systems and representations of the group \mathbb Z. In the second part, we deal with regular-singular connections over R((x)) and \mathbb PR1\smallsetminus\0,∞\, where R=C[[t1,…,tr]]/I. The picture we offer shows that regular-singular connections are equivalent to representations of \mathbb Z, now over R.