## View abstract

### Session S26 - Finite fields and applications

Friday, July 16, 11:30 ~ 11:50 UTC-3

## On integral points on isotrivial elliptic curves over function fields

### Ricardo Conceicao

#### Gettysburg College, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakf08dc50bf6881665a8b4b07ce38178f2').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyf08dc50bf6881665a8b4b07ce38178f2 = 'rc&#111;nc&#101;&#105;c' + '&#64;'; addyf08dc50bf6881665a8b4b07ce38178f2 = addyf08dc50bf6881665a8b4b07ce38178f2 + 'g&#101;ttysb&#117;rg' + '&#46;' + '&#101;d&#117;'; var addy_textf08dc50bf6881665a8b4b07ce38178f2 = 'rc&#111;nc&#101;&#105;c' + '&#64;' + 'g&#101;ttysb&#117;rg' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakf08dc50bf6881665a8b4b07ce38178f2').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyf08dc50bf6881665a8b4b07ce38178f2 + '\'>'+addy_textf08dc50bf6881665a8b4b07ce38178f2+'<\/a>';

Let $k$ be a finite field and $L$ be the function field of a curve $C/k$. In this talk, we discuss certain arithmetical properties satisfied by integral points on elliptic curves over $L$ such that their $j$-invariant is an element of $k$. One particular result that we prove is that the number of separable $S$-integral points on a constant elliptic curve $E/L$ is bounded solely in terms of the size of $S$ and the genus of $C$.