Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 2 (2019), 379-424.
Functorial factorization of birational maps for qe schemes in characteristic 0
We prove functorial weak factorization of projective birational morphisms of regular quasiexcellent 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, answering a present need in nonarchimedean geometry. Techniques developed for this purpose include a method for functorial factorization of toric maps, variation of GIT quotients relative to general noetherian qe schemes, and a GAGA theorem for Stein compacts.
Algebra Number Theory, Volume 13, Number 2 (2019), 379-424.
Received: 20 December 2017
Revised: 23 November 2018
Accepted: 4 January 2019
First available in Project Euclid: 26 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14E05: Rational and birational maps
Secondary: 14A20: Generalizations (algebraic spaces, stacks) 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 32H04: Meromorphic mappings
Abramovich, Dan; Temkin, Michael. Functorial factorization of birational maps for qe schemes in characteristic 0. Algebra Number Theory 13 (2019), no. 2, 379--424. doi:10.2140/ant.2019.13.379. https://projecteuclid.org/euclid.ant/1553565646