Functorial factorization of birational maps for qe schemes in characteristic 0

Abramovich, Dan; Temkin, Michael

doi:10.2140/ant.2019.13.379

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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

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.

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

Vol. 13, No. 2, 2019