The direct summand conjecture in dimension three
By R. Heitmann. 2002
101 citations recorded by the source corpus.
The direct summand conjecture asserts that if R is a regular local ring and S is a module-finite R-algebra containing R, then R is a direct summand of S as an R-module. It was previously known to be true if R contains a field or if dim R is at most two. In this article, the result is demonstrated for mixed characteristic rings of dimension three. The proof is accomplished by showing that an extension of plus closure has the colon-capturing property in dimension three.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/cef40a458e9dbc654e6fff4442699982a170d607
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In Algebra and Number Theory
In Geometry and Topology
- B. Bhatt
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- Peter Scholze
- Wiesława Nizioł
- Arpon Raksit
- Ruochuan Liu
- Kiran S. Kedlaya
- Bertrand Toën
Citations in the corpus
- Derived splinters in positive characteristic (2011, background): “he still open direct summand conjecture [Hoc73] posits that all regular rings are splinters; this conjecture is known in equicharacteristic by [Hoc73] or in mixed characteristic for dimensions ≤ 3 by [Hei02], but is unknown in general, and is a fundamental open problem in the subject. Our definition ”