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arXiv · 2404.17572

On liftings of modules of finite projective dimension

Nawaj KC·Andrew J. Soto Levins
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Abstract

We introduce and study a notion of Serre liftable modules; these are modules that are liftable to modules of the maximal possible dimension over a regular local ring. We establish new cases of Serre's positivity conjecture over ramified regular local rings by proving it for Serre liftable modules. Furthermore, we show that the length of a nonzero Serre liftable module is bounded below by the Hilbert-Samuel multiplicity of the local ring. This establishes special cases of the Length Conjecture of Iyengar-Ma-Walker.

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Nawaj KC, Andrew J. Soto Levins. 2024-04-26. On liftings of modules of finite projective dimension. https://arxiv.org/abs/2404.17572

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