Almost proper GIT-stacks and discriminant avoidance.
Étale cohomology of rigid analytic spaces.
Families of curves and alterations
In this article it is shown that any family of curves can be altered into a semi-stable family. This implies that if is an excellent scheme of dimension at most 2 and is a separated integral scheme of finite type over , then can be altered into a regular scheme. This result is stronger then the results of [ Smoothness, semi-stability and alterations to appear in Publ. Math. IHES]. In addition we deal with situations where a finite group acts.
Crystalline Dieudonné theory over excellent schemes
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