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2019 Functorial factorization of birational maps for qe schemes in characteristic 0
Dan Abramovich, Michael Temkin
Algebra Number Theory 13(2): 379-424 (2019). DOI: 10.2140/ant.2019.13.379

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.

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Dan Abramovich. Michael Temkin. "Functorial factorization of birational maps for qe schemes in characteristic 0." Algebra Number Theory 13 (2) 379 - 424, 2019. https://doi.org/10.2140/ant.2019.13.379

Information

Received: 20 December 2017; Revised: 23 November 2018; Accepted: 4 January 2019; Published: 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07042063
MathSciNet: MR3927050
Digital Object Identifier: 10.2140/ant.2019.13.379

Subjects:
Primary: 14E05
Secondary: 14A20 , 14E15 , 14L30 , 32H04

Keywords: bimeromorphic maps , birational geometry , blowing up

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2019
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