On Base Change of Local Stability in Positive Characteristics

2020/01/13 by Zhi Hu, Hu, Zhi, Runhong Zong +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2001.04083

openalex publication_date 2020/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a pointed one dimensional family of varieties X→ b∈ B in positive characteristics is locally stable iff the log pair (X', X'_b') arising from its base change to the perfectoid base b'∈ B_perf is log canonical.

Related

• Base-change of locally stable families in positive characteristic
• Log canonical singularities and complete moduli of stable pairs
• Extensions of two Chow stability criteria to positive characteristics
• Log canonical thresholds in positive characteristic
• Logarithmic base change theorem and smooth descent of positivity of log canonical divisor