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arXiv · 1610.05674

The $p$-curvature conjecture and monodromy about simple closed loops

Ananth N. Shankar
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Abstract

The Grothendieck-Katz $p$-curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its $p$-curvature vanishes modulo $p$, for almost all primes $p$. We prove that if the variety is a generic curve, then every simple closed loop on the curve has finite monodromy.

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Ananth N. Shankar. 2016-10-18. The $p$-curvature conjecture and monodromy about simple closed loops. https://doi.org/10.1215/00127094-2018-0008

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