Lundi 12 Septembre 2011

15h30-16h30 Y. Tian (Morningside Center of Mathematics)

Classicality of overconvergent Hilbert modular forms in the quadratic inert case

A classical theorem of Coleman says that an overconvergent (elliptic) p-adic eigenform of small slope is classical. Now consider a quadratic real field F and a prime p that is inert in F. Let f be an overconvergent p-adic Hilbert eigenform for F. In this talk, we show that f is classical if its slope is strictly smaller than min(k_1,k_2)-2.