Valuation rings are derived splinters
Algebraic Geometry
2020-02-05 v1 Commutative Algebra
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.
Cite
@article{arxiv.2002.01067,
title = {Valuation rings are derived splinters},
author = {Benjamin Antieau and Rankeya Datta},
journal= {arXiv preprint arXiv:2002.01067},
year = {2020}
}
Comments
24 pages; comments very welcome