On the quasicompactness of the moduli stack of logarithmic G-connections over a curve

TL;DR

This paper proves that the moduli stack of G-bundles with logarithmic connections and fixed residues over a smooth projective curve is algebraic and of finite type, advancing understanding of their geometric structure.

Contribution

It establishes the algebraic and finite type nature of the moduli stack of G-bundles with fixed residues and logarithmic connections over a curve, a new result in the field.

Findings

The moduli stack is algebraic.

The moduli stack is of finite type.

Fixed residue classes are compatible with the stack's structure.

Abstract

Fix a smooth projective curve over a field of characteristic zero and a finite set of punctures. Let G be a connected linear algebraic group. We prove that the moduli of G-bundles with logarithmic connections having fixed residue classes at the punctures is an algebraic stack of finite type.