1. CJM 2016 (vol 68 pp. 1362)
||Optimal Quotients of Jacobians with Toric Reduction and Component Groups|
Let $J$ be a Jacobian variety with toric reduction
over a local field $K$.
Let $J \to E$ be an optimal quotient defined over $K$, where
$E$ is an elliptic curve.
We give examples in which the functorially induced map $\Phi_J
on component groups of the NÃ©ron models is not surjective.
This answers a question of Ribet and Takahashi.
We also give various criteria under which $\Phi_J \to \Phi_E$
is surjective, and discuss
when these criteria hold for the Jacobians of modular curves.
Keywords:Jacobians with toric reduction, component groups, modular curves
Categories:11G18, 14G22, 14G20
2. CJM 2014 (vol 67 pp. 893)
||Overconvergent Families of Siegel-Hilbert Modular Forms|
We construct one-parameter families of overconvergent Siegel-Hilbert
modular forms. This result has applications to construction of
Galois representations for automorphic forms of non-cohomological
Keywords:p-adic automorphic form, rigid analytic geometry