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arXiv · 2512.18506

Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings

Yotam Svoray
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Abstract

This paper develops a theory of isolated hypersurface singularities in mixed characteristic $(0,p)$, focusing on quotient rings over a Discrete Valuation Ring (DVR). We introduce and study analogues of the classical Tjurina and Milnor numbers for this setting, prove a generalized analogue of the determinacy theorem and the Mather-Yau Theorem for complete Noetherian local rings, and define numerical invariants that provide distinct criteria for detecting isolated singularities in the unramified and ramified cases.

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Yotam Svoray. 2025-12-20. Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings. https://arxiv.org/abs/2512.18506

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