Ranks of abelian varieties over function fields

Mardi 2 octobre 2007 16:00-17:00 - Ulmer Douglas - University of Arizona et Orsay

Résumé : Recently I gave a construction, for each prime p and each integer g>0, of abelian varieties of dimension g over the rational function field $F_p(t)$ which satisfy the conjecture of Birch and Swinnerton-Dyer and which have arbitrarily large groups of rational points. I will sketch the main ideas and then give a variant construction which produces families of abelian varieties as above and which may also be useful when $F_p$ is replaced by a field of characteristic zero.

Lieu : bât. 425 - 113-115

Ranks of abelian varieties over function fields  Version PDF