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

Ananth Shankar , Harvard University
IAS Room S101
The GrothendieckKatz pcurvature 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 pcurvature 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.