## View abstract

### Session S26 - Finite fields and applications

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

## On the generalized Suzuki curve

### Mariana Coutinho

#### Universidade de São Paulo, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak11dcae5506018618a2e86accbe795134').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy11dcae5506018618a2e86accbe795134 = 'm&#97;r&#105;&#97;n&#97;n&#101;ry' + '&#64;'; addy11dcae5506018618a2e86accbe795134 = addy11dcae5506018618a2e86accbe795134 + '&#97;l&#117;mn&#105;' + '&#46;' + '&#117;sp' + '&#46;' + 'br'; var addy_text11dcae5506018618a2e86accbe795134 = 'm&#97;r&#105;&#97;n&#97;n&#101;ry' + '&#64;' + '&#97;l&#117;mn&#105;' + '&#46;' + '&#117;sp' + '&#46;' + 'br';document.getElementById('cloak11dcae5506018618a2e86accbe795134').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy11dcae5506018618a2e86accbe795134 + '\'>'+addy_text11dcae5506018618a2e86accbe795134+'<\/a>';

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.

Joint work with Herivelto Borges (Universidade de São Paulo, Brazil).