The p-radical closure of local noetherian rings

2016/10/27 by Schröer, Stefan · 2 citations
#13B22 #13F40 #13J10 #14JA05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.08675

Abstract

Given a local noetherian ring R whose formal completion is integral, we introduce and study the p-radical closure R^prc. Roughly speaking, this is the largest purely inseparable R-subalgebra inside the formal completion R. It turns out that the finitely generated intermediate rings R⊂ A⊂ R^prc have rather peculiar properties. They can be used in a systematic way to provide examples of integral local rings whose normalization is non-finite, that do not admit a resolution of singularities, and whose formal completion is non-reduced.

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• K3 surfaces over small number fields and Kummer constructions in families
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