MSc Mathematics Pre-thesis Seminar
Date: Friday, 10 November 2023
Time: 10.30 - 11.30 AM
Venue: Lecture Hall 202
Regular Primes and Herbrand's Theorem
Atharva Raje
Chennai Mathematical Institute.
10-11-23

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Abstract

In 1847, Kummer proved Fermat’s Last Theorem for regular primes p, that is, that the Diophantine equation $x^{p} + y^{p} = z^{p}$ has no solutions in positive integers. Kummer further provided a necessary and sufficient condition for a prime to be regular in terms of the divisibility of Bernoulli numbers by the prime. The Herbrand Ribet Theorem is a stronger version of Kummer’s criterion, relating specific Bernoulli numbers divisible by p to corresponding non-trivial p-torsion components of the class group of the cyclotomic field $\Q(\zeta_{p})$. In this talk, we will examine the proof of one direction of this theorem, due to Herbrand, reviewing some preliminary ideas along the way.