Equivariant cd-structures and descent theory

TL;DR

This paper introduces equivariant cd-structures to develop descent theory for various topologies, enabling proofs of descent results that traditional structures cannot achieve, with applications to log schemes.

Contribution

It constructs equivariant cd-structures and develops descent theory for associated topologies, extending the scope of descent results beyond traditional cd-structures.

Findings

Reproved results on étale, qfh, and h descent using equivariant cd-structures.

Extended descent theory to topologies not arising from usual cd-structures.

Applied equivariant cd-structures to study topologies on noetherian fs log schemes.

Abstract

We construct the equivariant version of cd-structures, and we develop descent theory for topologies comes from equivariant cd-structures. In particular, we reprove several results of Cisinski-D\'eglies on the \'etale descent, qfh-descent, and h-descent. Since the \'etale topos, qfh-topos, and h-topos do not come from usual cd-structures, such results cannot be produced by usual cd-structures. We also apply equivariant cd-structures to study several topologies on the category of noetherian fs log schemes.