# Sur les repr\'esentations du groupe fondamental d'une vari\'et\'e priv\'ee d'un diviseur \`a croisements normaux simples

## TL;DR

This paper establishes a correspondence between finite parabolic bundles on a projective variety with a simple normal crossings divisor and representations of the étale fundamental group of the complement, enriching the understanding of fundamental group representations.

## Contribution

It proves a bijective correspondence between parabolic bundles and fundamental group representations in the context of varieties with normal crossings divisors.

## Key findings

- Finite parabolic bundles correspond to étale fundamental group representations.
- The correspondence applies to projective varieties over algebraically closed fields of characteristic zero.
- Provides a new perspective on the relationship between geometric bundles and algebraic fundamental groups.

## Abstract

Given a projective variety X over an algebraically closed field of characteristic zero, we show that finite parabolic bundles along a fixed simple normal crossings divisor D are in one to one correspondence with representations of the \'etale fundamental group of X-D.