Formal lifting of dualizing complexes and consequences

2023/11/30 by Lyu, Shiji · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.18196

Abstract

We show that for a Noetherian ring A that is I-adically complete for an ideal I, if A/I admits a dualizing complex, so does A. This gives an alternative proof of the fact that a Noetherian complete local ring admits a dualizing complex. We discuss several consequences of this result. We also consider a generalization of the notion of dualizing complexes to infinite-dimensional rings and prove the results in this generality. In addition, we give an alternative proof of the fact that every excellent Henselian local ring admits a dualizing complex, using ultrapower.

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• The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

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