Kiran S. Kedlaya

Title:A p-adic local monodromy theorem

Differential equations on non-simply-connected domains arise in the complex setting in Hodge theory, and in the p-adic setting in the work of Dwork and his followers. In particular, one would like to know conditions under which a p-adic differential equation on an annulus becomes nilpotent after a finite base change. Richard Crew conjectured that it would suffice for the equation to admit a "Frobenius structure". We explain what this means, sketch a proof of his conjecture, and mention some applications.