Prolongement analytique sur les variétés de Siegel

Pilloni, Vincent

Duke Math. J., Tome 156 (2011) no. 1, p. 167-222 / Harvested from Project Euclid

Résumé

We study analytic continuation of overconvergent modular forms on Siegel varieties. We first analyze the dynamic of Hecke correspondances at

$p$ over Siegel varieties with parahoric-level structure. We then concentrate on genus

$2$ and prove a classicity criterion: a Siegel overconvergent modular form, of weight

$(k_1,k_2)$ , eigen for

$U_p$ with eigenvalue

$a_p$ , such that

$k_2 > v(a_p)+3$ is classical. This implies that genus

$2$ cuspidal ordinary

$p$ -adic modular forms of weight

$(k_1,k_2)$ with

$k_1 \geq k_2 \geq 4$ are classical.

Publié le : 2011-03-15
Classification: 11F46, 14G35

@article{1300281535,
     author = {Pilloni, Vincent},
     title = {Prolongement analytique sur les vari\'et\'es de Siegel},
     journal = {Duke Math. J.},
     volume = {156},
     number = {1},
     year = {2011},
     pages = { 167-222},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300281535}
}

Pilloni, Vincent. Prolongement analytique sur les variétés de Siegel. Duke Math. J., Tome 156 (2011) no. 1, pp.  167-222. http://gdmltest.u-ga.fr/item/1300281535/