Vol. 13, No. 2, 2019

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Functorial factorization of birational maps for qe schemes in characteristic 0

Dan Abramovich and Michael Temkin

Vol. 13 (2019), No. 2, 379–424
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.

Keywords
birational geometry, blowing up, bimeromorphic maps
Mathematical Subject Classification 2010
Primary: 14E05
Secondary: 14A20, 14E15, 14L30, 32H04
Milestones
Received: 20 December 2017
Revised: 23 November 2018
Accepted: 4 January 2019
Published: 2 March 2019
Authors
Dan Abramovich
Department of Mathematics
Brown University
Providence, RI
United States
Michael Temkin
Einstein Institute of Mathematics
The Hebrew University of Jerusalem
Jerusalem
Israel