Algebra & Number Theory

Functorial factorization of birational maps for qe schemes in characteristic 0

Dan Abramovich and Michael Temkin

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Abstract

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.

Article information

Source
Algebra Number Theory, Volume 13, Number 2 (2019), 379-424.

Dates
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
https://projecteuclid.org/euclid.ant/1553565646

Digital Object Identifier
doi:10.2140/ant.2019.13.379

Mathematical Reviews number (MathSciNet)
MR3927050

Zentralblatt MATH identifier
07042063

Subjects
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

Keywords
birational geometry blowing up bimeromorphic maps

Citation

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


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