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arXiv · 2501.07528

Plus-pure thresholds of some cusp-like singularities in mixed characteristic

Hanlin Cai·Suchitra Pande·Eamon Quinlan-Gallego·Karl Schwede·Kevin Tucker
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Abstract

Log-canonical and $F$-pure thresholds of pairs in equal characteristic admit an analog in the recent theory of singularities in mixed characteristic, which is known as the plus-pure threshold. In this paper we study plus-pure thresholds for singularities of the form $p^a + x^b \in {\bf Z}_p [[ x ]]$, showing that in a number of cases this plus-pure threshold agrees with the $F$-pure threshold of the singularity $t^a + x^b \in {\bf F}_p [[ t, x ]]$. We also discuss a few other sporadic examples.

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Hanlin Cai, Suchitra Pande, Eamon Quinlan-Gallego, Karl Schwede, Kevin Tucker. 2025-01-13. Plus-pure thresholds of some cusp-like singularities in mixed characteristic. https://arxiv.org/abs/2501.07528

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