Reductions towards a characteristic free proof of the Canonical Element Theorem

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 w...

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Bibliographic Details
Published in:Journal of algebra 2023-10, Vol.631, p.558-609
Main Author: Tavanfar, Ehsan
Format: Article
Language:English
Subjects:
Almost complete intersection ring
Balanced big Cohen-Macaulay module
Canonical Element Theorem
Direct Summand Theorem
Extended Rees algebra
Improved New Intersection Theorem
Monomial Theorem
Quasi-Gorenstein ring
Unique factorization domain
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2023.05.007