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arXiv · 2403.15566

Non-existence of Ulrich modules over Cohen-Macaulay local rings

Srikanth B. Iyengar·Linquan Ma·Mark E. Walker·Ziquan Zhuang
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Abstract

Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there always exist modules for which equality holds; such modules are known nowadays as Ulrich modules. We answer this question in the negative by constructing families of two dimensional Cohen-Macaulay local rings that have no Ulrich modules. Some of these examples are Gorenstein normal domains; others are even complete intersection domains, though not normal.

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Srikanth B. Iyengar, Linquan Ma, Mark E. Walker, Ziquan Zhuang. 2024-03-22. Non-existence of Ulrich modules over Cohen-Macaulay local rings. https://arxiv.org/abs/2403.15566

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