Time: 16:00-17:30, Tuesday, April 14 2026
Venue: E14-222
Speaker: Wojciech Porowski, RIMS, Kyoto University
Title: Families of curves separating points
Abstract: Let X be a hyperbolic curve over an algebraically closed field k. Let S be a finite subset of the set of k-rational points of X. We consider the following problem:
Does there exist a family of curves Y->X over X s such that the Jacobians of fibres over points in S are pairwise non isogenous?
In the first part of the talk, working in characteristic zero, we will sketch a positive solution to this problem after passing a finite etale cover of X. In the second part we will discuss an application of this method to a problem concerning Galois sections.
