
TL;DR
This paper demonstrates how recent advances in p-adic Hodge theory can be used to prove new cases of Hochster's direct summand conjecture, especially in characteristic p ramification scenarios.
Contribution
It introduces a novel approach linking p-adic Hodge theory to the direct summand conjecture, expanding the known cases where the conjecture holds.
Findings
New cases of Hochster's conjecture are established in characteristic p.
Fundamental p-adic Hodge theorems are applied to commutative algebra problems.
The approach simplifies proofs of certain direct summand cases.
Abstract
In this short note, we point out how some new cases of Hochster's direct summand conjecture can be deduced from fundamental theorems in p-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification of the map being considered lies entirely in characteristic p.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
