#### Number Theory Seminar

##### Venue: Microsoft Teams (Online)

In his 1976 proof of the converse to Herbrand’s theorem, Ribet used Eisenstein-cuspidal congruences to produce unramified degree-$p$ extensions of the $p$-th cyclotomic field when $p$ is an odd prime. After reviewing Ribet’s strategy, we will discuss recent work with Preston Wake in which we apply similar techniques to produce unramified degree-$p$ extensions of $\mathbb{Q}(N^{1/p})$ when $N$ is a prime that is congruent to $-1$ mod $p$. This answers a question posted on Frank Calegari’s blog.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 03 Feb 2023