## STNB2019 (33rd edition)

### On the asymptotic Fermat Last Theorem

#### Presenters

Nuno Freitas

#### Abstract

Let $K$ be a number field. The asymptotic Fermat's Last Theorem (AFLT)
states that there exists a constant $B_K$, depending only on $K$, such that
for all prime numbers $p > B_K$ all the solutions to the Fermat equation
$x^p + y^p = z^p$ satisfy $xyz = 0$.

In this talk we will discuss how this relates to the non-existence of certain elliptic
curves over $K$ and sketch the proof of AFLT over infinitely many fields, including
all the layers of the $\mathbb{Z}_2$-extesion of $\mathbb{Q}$.

This is joint work with Alain Kraus and Samir Siksek.

#### Files

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