Functorial factorization of birational maps for qe schemes in characteristic 0

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.

45 pages

References in corpus (2)

• The tropicalization of the moduli space of curves
• Desingularization of quasi-excellent schemes in characteristic zero

Cited by in corpus (4)

• Functorial embedded resolution via weighted blowings up
• Motivic integration and the birational invariance of BCOV invariants
• Betti realization of varieties defined by formal Laurent series
• A motivic integral $p$-adic cohomology