Algebraic and Arithmetic Geometry Seminar: "The algebraic geometry of the Putman-Wieland conjecture"
Speaker: Aaron Landesman, Harvard University
Abstract: Suppose we are given a family of finite \'etale covers $X \to Y$ from a genus $g'$ curve to a genus $g \geq 2$ curve, so that a general genus $g$ curve appears in this family. The Putman-Wieland conjecture predicts that there is no common isogeny factor in the Jacobian of every such $X$. Based on joint work with Daniel Litt, we describe how to establish many new cases of the Putman-Wieland conjecture by relating the derivative of an associated period map to properties of canonically embedded curves.
Host: Matt Kerr