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arXiv · 2503.20115

Characterising properties of commutative rings using Witt vectors

Rubén Muñoz--Bertrand
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Abstract

We give equivalences between given properties of a commutative ring, and other properties on its ring of Witt vectors. Amongst them, we characterise all commutative rings whose rings of Witt vectors are Noetherian. We define a new category of commutative rings called preduced rings, and explain how it is the category of rings whose ring of Witt vectors has no $p$-torsion. We then extend this characterisation to the torsion of the de Rham-Witt complex.

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Rubén Muñoz--Bertrand. 2025-03-25. Characterising properties of commutative rings using Witt vectors. https://arxiv.org/abs/2503.20115

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