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Remarks on logarithmic \'etale sheafification

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arxiv 2311.05172 v1 pith:W2M6MYF3 submitted 2023-11-09 math.AG

Samouil Molcho , Jonathan Wise This is my paper · ORCID
classification math.AG
keywords logarithmicetalestructurefullschemessheafsheavestopology
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We prove criteria for a presheaf on logarithmic schemes to be a sheaf in the full logarithmic \'etale topology and describe several situations where the structure sheaf and logarithmic structure are logarithmic \'etale sheaves. We deduce that the logarithmic Picard group is a stack in the full logarithmic \'etale topology on logarithmic schemes whose structure sheaves satisfy logarithmic \'etale descent.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The log Grothendieck ring of varieties

    math.AG 2024-12 conditional novelty 8.0 of 10

    The log Grothendieck ring of varieties is K0(Var)[P]/(P^2+P[G_m]), and a log chi-y genus built from it is motivic even though log Hodge numbers are not.

  2. On the $K$-theoretic logarithmic double ramification class

    math.AG 2026-07 conditional novelty 7.0 of 10

    A K-theoretic logarithmic double ramification class is constructed, shown to satisfy a GL_r(Z)-invariant product formula in colimit log K-theory, and computed by a new stack-valued Thom–Porteous formula.

  3. Grothendieck topologies with logarithmic modifications

    math.AG 2025-10 conditional novelty 6.0 of 10

    New 'logarithmic modification' topologies for fs log schemes are defined, with sheaf characterizations and a claimed correction to the full log étale site.

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