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arXiv · 2201.13002

Torsion in Differentials and Berger's Conjecture

Craig Huneke·Sarasij Maitra·Vivek Mukundan
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Abstract

Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over an algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only if the universally finite module of differentials $\Omega_R$ is a torsion-free $R$-module. We give new cases of this conjecture by extending works of G\"uttes (Arch Math 54:499-510, 1990) and Corti\~nas et al. (Math Z 228:569-588, 1998).This is obtained by constructing a new subring $S$ of $\operatorname{Hom}_R(\mathfrak{m},\mathfrak{m})$ and constructing enough torsion in $\Omega_S$, enabling us to pull back a nontrivial torsion to $\Omega_R$.

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Craig Huneke, Sarasij Maitra, Vivek Mukundan. 2022-01-31. Torsion in Differentials and Berger's Conjecture. https://doi.org/10.1007/s40687-021-00295-y

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