Semistable reduction in characteristic 0

2018/10/07 by Adiprasito, Karim, Liu, Gaku, Temkin, Michael · 1 citation
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.03131

Abstract

In 2000 Abramovich and Karu proved that any dominant morphism f X→ B of varieties of characteristic zero can be made weakly semistable by replacing B by a smooth alteration B' and replacing the proper transform of X by a modification X'. In the language of log geometry this means that f' X'→ B' is log smooth and saturated for appropriate log structures. Moreover, Abramovich and Karu formulated a stronger conjecture that f' X'→ B' can be even made semistable, which amounts to making X' smooth as well, and explained why this is the best resolution of f one might hope for. In this paper, we solve the semistable reduction conjecture in the larger generality of finite type morphisms of quasi-excellent schemes of characteristic zero.

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