Tame derivatives and the Eisenstein ideal

Abstract: As was made famous by Mazur, the mod-5 Galois representation associated to the elliptic curve $X_0(11)$ is reducible. Less famously, but also noted by Mazur, the mod-25 Galois representation is reducible. We'll explain why this mod-5 reducibility is to be expected, but why this mod-25 reducibility is surprising. We'll also discuss the analytic and algebraic significance of the characters that appear in the mod-25 representation.

number theory

Audience: researchers in the topic

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11