|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||The $p$-curvature conjecture and monodromy about simple closed loops|
|Date:||Thursday, May 11|
|Time/Room:||4:30pm - 5:30pm/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.