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arXiv · 2002.01067

Valuation rings are derived splinters

Benjamin Antieau·Rankeya Datta
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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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Benjamin Antieau, Rankeya Datta. 2020-02-04. Valuation rings are derived splinters. https://arxiv.org/abs/2002.01067

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