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

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Ananth Shankar , Harvard University
IAS Room S-101

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 has finite monodromy.