Reductions towards a characteristic free proof of the Canonical Element Theorem
Abstract
We reduce Hochster's Canonical Element Conjecture (theorem since 2016) to a localization problem in a characteristic free way. We prove the validity of a new variant of the Canonical Element Theorem (CET) and explain how a characteristic free deduction of the new variant from the original CET would provide us with a characteristic free proof of the CET. We also show that the Balanced Big Cohen-Macaulay Module Theorem can be settled by a characteristic free proof if the big Cohen-Macaulayness of Hochster's modification module can be deduced from the existence of a maximal Cohen-Macaulay complex in a characteristic-free way.
Keywords
Cite
@article{arxiv.2203.05327,
title = {Reductions towards a characteristic free proof of the Canonical Element Theorem},
author = {Ehsan Tavanfar},
journal= {arXiv preprint arXiv:2203.05327},
year = {2023}
}
Comments
Accepted for publication in Journal of Algebra. The last version (38 pages), thanks to the referee, has improved presentation and the proof of a few results are simplified. Also, Remark 5.3 is added and Remark 5.4 is improved