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On Base Change of Local Stability in Positive Characteristics

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arxiv 2001.04083 v1 pith:LP2RNBLY submitted 2020-01-13 math.AG

Zhi Hu , Runhong Zong This is my paper · ORCID
classification math.AG
keywords basemathcalchangecharacteristicspositivearisingcanonicaldimensional
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abstract

We prove that a pointed one dimensional family of varieties $\mathcal{X}\to {b\in B}$ in positive characteristics is locally stable iff the log pair $(\mathcal{X'}, \mathcal{X}'_{b'})$ arising from its base change to the perfectoid base $b'\in B_{perf}$ is log canonical.

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  1. Pathological MMP singularities as $\alpha_p$-quotients

    math.AG 2025-01 conditional novelty 8.0 of 10

    For every positive characteristic, the author constructs non-S3 terminal singularities of dimension p+1 and stable families with klt, Cohen-Macaulay, F-injective general fibers but non-S2 special fibers.

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