Contractibility of the space of generic opers for classical groups

TL;DR

This paper proves that the space of generic extended oper structures for classical groups on a smooth projective curve is homologically contractible, which is a key step in establishing the geometric Langlands conjecture.

Contribution

It establishes the homological contractibility of the space of generic extended oper structures for classical groups, advancing the geometric Langlands program.

Findings

Homological contractibility of the space of generic extended opers.

Crucial step for the proof of the geometric Langlands conjecture.

Applicable to classical groups on smooth projective curves.

Abstract

Let $G$ be a reductive group and $X$ a smooth projective curve. We prove that, for $G$ classical and $\sigma$ an arbitrary $G$-local system on $X$, the space $\overline{\operatorname{Op}}^{gen}_{G,\sigma}$ of generic extended oper structures on $\sigma$ is homologically contractible. This contractibility result is crucial for the proof of the geometric Langlands conjecture.