## View abstract

### Session S26 - Finite fields and applications

Friday, July 16, 12:00 ~ 12:20 UTC-3

## On the generalized Suzuki curve

### Mariana Coutinho

Let $p$ be a prime number and, for $t>1$, consider $\mathcal{X}$ the nonsingular model of $$Y^{q}-Y= X^{q_0}(X^{q}- X),$$ where $q_{0}= p^{t}$ and $q=p^{2t-1}$.
For $p$ even, $\mathcal{X}$ is the so-called Deligne--Lusztig curve associated with the Suzuki group, which has remarkable properties, for instance its large automorphism group with respect to the genus.
In the present work, we address the study of $\mathcal{X}$ for $p$ an odd prime number.