Criterion for the nonexistence of rational $p$-torsion

Abstract: Reduce the proof of the main theorem to showing that there exists a rank-$0$ quotient $A$ of $J_0(p)$ such that $[0]\ne [\infty]$ in $A$.

Reference: [Ma1] Section III.5

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2026 topic: Explicit class field theory.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.