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arXiv · 2203.05327

Reductions towards a characteristic free proof of the Canonical Element Theorem

Ehsan Tavanfar
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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.

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Ehsan Tavanfar. 2023-05-09. Reductions towards a characteristic free proof of the Canonical Element Theorem. https://doi.org/10.1016/j.jalgebra.2023.05.007

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