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$p$-integrability

Published 29 Jul 2025 in math.AG and math.NT | (2507.22056v1)

Abstract: In this short note, we prove the equivalence of Grothendieck-Katz $p$-curvature Conjecture with Conjecture F in Ekedahl-Shepherd-Barron-Taylor. More precisely, we show that Conjecture F implies the $p$-curvature conjecture, and that the $p$-curvature Conjecture implies Conjecture F for the foliation attached to a vector bundle with integrable connection.

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