Valuation rings are derived splinters

2020/02/04 by Antieau, Benjamin, Datta, Rankeya · 1 citation
#13A18 #13D09 #13D22 #14B05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.01067

Abstract

We give three proofs that valuation rings are derived splinters: a geometric proof using the absolute integral closure, a homological proof which reduces the problem to checking that valuation rings are splinters (which is done in the second author's PhD thesis and which we reprise here), and a proof by approximation which reduces the problem to Bhatt's proof of the derived direct summand conjecture. The approximation property also shows that smooth algebras over valuation rings are splinters.

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