Bounding ramification with covers and curves

Abstract: In positive characteristic, there is no curve with the property that its fundamental group covers the one of a given variety $X$ (Lefschetz property). Deligne asked whether over an algebraically closed field there is such a curve which preserves the monodromy groups of ${\bar \mathbb{Q}}_\ell$ local systems in bounded rank and ramification on $X$. We can not prove this in general, instead we give weaker statements which enable one to tamify local systems.

Joint work with Vasudevan Srinivas.

algebraic geometrynumber theory

Audience: researchers in the discipline

Upstate New York Online Number Theory Colloquium