Ramified Galois covers via monoidal functors

TL;DR

This paper develops a new categorical framework for understanding Galois covers using monoidal functors, leading to characterizations of tame covers and insights into the structure of moduli stacks for nonabelian group schemes.

Contribution

It introduces a novel interpretation of Galois covers via monoidal functors, extending classical torsor-fiber functor correspondence and analyzing moduli stack reducibility.

Findings

Characterization of tame G-covers between normal varieties.

Proof that the moduli stack of G-covers is reducible for certain nonabelian group schemes.

Extension of torsor correspondence to a broader categorical context.

Abstract

We interpret Galois covers in terms of particular monoidal functors, extending the correspondence between torsors and fiber functors. As applications we characterize tame $G$-covers between normal varieties for finite and \'etale group schemes and we prove that, if $G$ is a finite, flat and finitely presented nonabelian and linearly reductive group scheme over a ring, then the moduli stack of $G$-covers is reducible.