Kisin, MarkShankar, Ananth2019-05-202017-052017-04-272017http://nrs.harvard.edu/urn-3:HUL.InstRepos:40046427The Grothendieck-Katz p-curvature 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.application/pdfenMathematicsThesis or Dissertation2019-05-20