## View abstract

### Session S09 - Number Theory in the Americas

Wednesday, July 14, 13:30 ~ 14:00 UTC-3

## Rational approximation and extension of scalars

### Damien Roy

#### U. Ottawa, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloaka8a8e33ca60e2a9439986944a8bb594a').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addya8a8e33ca60e2a9439986944a8bb594a = 'd&#97;m&#105;&#101;n.r&#111;y' + '&#64;'; addya8a8e33ca60e2a9439986944a8bb594a = addya8a8e33ca60e2a9439986944a8bb594a + '&#117;&#111;tt&#97;w&#97;' + '&#46;' + 'c&#97;'; var addy_texta8a8e33ca60e2a9439986944a8bb594a = 'd&#97;m&#105;&#101;n.r&#111;y' + '&#64;' + '&#117;&#111;tt&#97;w&#97;' + '&#46;' + 'c&#97;';document.getElementById('cloaka8a8e33ca60e2a9439986944a8bb594a').innerHTML += '<a ' + path + '\'' + prefix + ':' + addya8a8e33ca60e2a9439986944a8bb594a + '\'>'+addy_texta8a8e33ca60e2a9439986944a8bb594a+'<\/a>';

We establish a new transference principle which, by extending scalars from $\mathbb{Q}$ to a number field, and by combination with a result of P. Bel, allows us to construct algebraic curves defined over $\mathbb{Q}$, of arbitrarily large degree, containing points that are very singular with respect to approximation by rational points. The results also admit interpretation in the setting of parametric geometry of numbers.

Joint work with Anthony Poels (U. Ottawa, Canada).