Hilbert Modular Forms : Mod P and P-Adic Aspects

Studies Hilbert modular forms in characteristic $p$ and over $p$-adic rings. This title describes the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; define operators $U$, $V$ and $Theta_chi$; and study the variation of the filtration under these operators.