Functorial factorization of birational maps for qe schemes in characteristic 0

TL;DR

This paper establishes a functorial weak factorization for projective birational morphisms of regular quasi-excellent schemes in characteristic 0, extending to various geometric contexts.

Contribution

It generalizes functorial factorization results from varieties to a broad class of schemes and related geometric objects.

Findings

Proves functorial weak factorization for regular quasi-excellent schemes in characteristic 0.

Extends factorization results to algebraic stacks, formal schemes, and analytic spaces.

Provides a unified approach based on existing proof techniques for varieties.

Abstract

We prove functorial weak factorization of projective birational morphisms of regular quasi-excellent schemes in characteristic 0 broadly based on the existing line of proof for varieties. From this general functorial statement we deduce factorization results for algebraic stacks, formal schemes, complex analytic germs, Berkovich analytic and rigid analytic spaces.