论文标题
$ r = t $定理的重量一个模块化表格
$R=T$ theorems for weight one modular forms
论文作者
论文摘要
我们证明了某些剩余可减少的普通二维$ p $ -Adic Galois表示的模块化，具有有限订单零件$χ$的决定性模块化。 For certain non-quadratic $χ$ we prove an $R=T$ result for $T$ the weight 1 specialisation of the Hida Hecke algebra acting on non-classical weight 1 forms, under the assumption that no two Hida families congruent to an Eisenstein series cross in weight 1. For quadratic $χ$ we prove that the quotient of $R$ corresponding to deformations split at $p$ is isomorphic to the Hecke代数作用于经典CM重量1模块化形式。
We prove modularity of certain residually reducible ordinary 2-dimensional $p$-adic Galois representations with determinant a finite order odd character $χ$. For certain non-quadratic $χ$ we prove an $R=T$ result for $T$ the weight 1 specialisation of the Hida Hecke algebra acting on non-classical weight 1 forms, under the assumption that no two Hida families congruent to an Eisenstein series cross in weight 1. For quadratic $χ$ we prove that the quotient of $R$ corresponding to deformations split at $p$ is isomorphic to the Hecke algebra acting on classical CM weight 1 modular forms.
