On extension of overconvergent log isocrystals on log smooth varieties

2020/06/25 by Kazumi Kasaura, Kasaura, Kazumi
Mathematics · #12H25 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.14203

openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By works of Kedlaya and Shiho, it is known that, for a smooth variety X over a field of positive characteristic and its simple normal crossing divisor Z, an overconvergent isocrystal on the compliment of Z satisfying a certain monodromy condition can be extended to a convergent log isocrystal on (X, M_Z), where M_Z is the log structure associated to Z. We prove a generalization of this result: for a log smooth variety (X,M) satisfying some conditions, an overconvergent log isocrystal on the trivial locus of a direct summand of M satisfying a certain monodromy condition can be extended to a convergent log isocrystal on (X, M).

Citations

• Logarithmic adic spaces: some foundational results

Related

• On logarithmic extension of overconvergent isocrystals
• Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions
• Cut-by-curves criterion for the log extendability of overconvergent isocrystals
• The monodromy of F-isocrystals with log-decay
• Log-decay F-isocrystals on higher dimensional varieties