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Congruences among Siegel and hermitian modular forms and the Bloch-Kato conjecture

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Krzysztof Klosin
U. Paris 13/MPI
Wed, 30/06/2010 - 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Let $f$ and $g$ be two cusp forms of weights $k$ and $2$ respectively. Let $\rho_f$ (resp. $\rho_g$) be the $p$-adic Galois representations attached to $f$ (resp. $g$). We will present two theorems (one of them work in progress with M. Agarwal) towards the Bloch-Kato conjecture for the motives $ad^0 \rho_f(-1)$ and $\rho_f \otimes \rho_g(-k/2-1)$. The method of the proof involves constructing congruences among either modular forms on the symplectic group of genus 2 or modular forms on the unitary group $U(2,2)$.

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