Geometric local systems on very general curves

Abstract: Conjectures of Esnault-Kerz and Budur-Wang state that the locus of rank r complex local systems on a complex variety of geometric origin are Zariski dense in the character variety parameterizing complex rank r local systems. In joint work with Daniel Litt, we show these conjectures fail to hold when X is a sufficiently general curve of genus $g$ and $r < 2\sqrt{g+1}$ by showing that any such local system coming from geometry is in fact isotrivial.

number theory

Audience: researchers in the topic

Harvard number theory seminar