Infinitely many rank 2 hyperelliptic curvesMPIM

by Stevan Gajovic (MPIM)

Wednesday Mar 18, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

Based on the recent result of Peter Koymans and Adam Morgan, who proved that there are infinitely many nonisomorphic hyperelliptic curves of any genus whose Jacobian has rank 1 over any number field, we prove the same result for rank 2; however, our curves do not have simple Jacobians, instead they factor into two rank 1 Jacobians. We also discuss results about higher rank Jacobians of small genus curves. This is joint work with Sun Woo Park.