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Colóquio dos Alunos

Título
Kummer’s special case of Fermat’s Last Theorem
Expositor
Santiago Arango Piñeros

IMPA
Data
Sexta-feira, 11 de maio de 2018, 15:30
Local
Sala 347
Resumo

One particularly elegant example of an application of modern algebraic number theory to a classical problem about the integers is found in Kummer’s special case of Fermat’s Last Theorem. In this talk, we will reduce Fermat’s Last Theorem to the question of whether or not there exist integer solutions to $x^p + y^p = z^p$ for $p$ an odd prime. We then give an exposition of Kummer’s proof that no such solutions exist in the case that $p$ does not divide the class number of $\mathbb{Q}(e^{2πi/p})$, that is when $p$ is a regular prime.