Zhi Hu, Runhong Zong
Abstract
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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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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.
Key concepts: Base change, Base (topology), Stability (learning theory), Mathematics, Combinatorics, Physics, Pure mathematics, Mathematical analysis