Tamely ramified torsors and parabolic bundles

TL;DR

This paper explores the relationship between tamely ramified torsors and parabolic bundles with prescribed weights on varieties with normal crossings divisors, focusing on cases with abelian monodromy.

Contribution

It establishes a connection between the existence of ramified torsors and finite parabolic bundles in the abelian monodromy setting.

Findings

Link between ramified torsors and parabolic bundles with prescribed weights

Conditions for existence of torsors with given ramification

Correspondence in the abelian monodromy case

Abstract

Given a variety $X$, and a normal crossings divisor $D\subset X$, we relate, in the case of abelian monodromy, the following two: 1. existence of a $G$-torsor with prescribed ramification, and 2. existence of essentially finite parabolic vector bundles with prescribed weights.