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Algebra Seminar

Friday, November 12, 2021 - 3:30pm

Jaclyn Lang

Temple University


University of Pennsylvania


One of two talks in the algebra seminar on this day. This talk is at the usual 3:30 time, and will be preceded by Alex Lubotzky's talk at 1:45. The talk will be simultaneously in person and on Zoom <p>Meeting ID: 935 4715 6018 Passcode: 209</p>

In his 1976 proof of the converse of 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 posed on Frank Calegari’s blog.

Meeting ID: 935 4715 6018
Passcode: 209