Monday, January 8, 2018
Algebra and Geometry Seminar
The p-curvature conjecture and monodromy around simple closed loops
Ananth Shankar, Department of Mathematics, MIT
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.