论文标题
有效的开放式图像定理，用于主要两极分化的阿伯利亚品种的产品
An effective open image theorem for products of principally polarized abelian varieties
论文作者
论文摘要
让$ a = \ prod_ {1 \ leq i \ leq n} a_i $是主要两极化的亚伯利亚品种的产物$ a_1，\ ldots，a_n $ dimensions $ g_1，\ ldots，g_n $，每个$ g_n $，每个定义在数字$ k $ k $ k的$ k $ and proppline $ and proppedline $ byperline $ byspline上。由于Hindry和Ratazzi，我们将有效的开放式图像定理定为$ a。 More specifically, we give an explicit bound of the constant $c(A)$ under GRH, in terms of standard invariants of $K$ and each $A_i$, where $c(A)$ is defined to be the smallest positive integer such that for any prime $\ell>c(A)$, the image of the $\ell$-adic Galois representation of $A$ is "as large as possible" in a suitable sense.
Let $A = \prod_{1\leq i\leq n} A_i$ be the product of principally polarized abelian varieties $A_1, \ldots, A_n$ of dimensions $g_1, \ldots, g_n$, respectively, each defined over a number field $K$, and pairwise nonisogenous over $\overline{K}$. We make effective an open image theorem for $A$ due to Hindry and Ratazzi. More specifically, we give an explicit bound of the constant $c(A)$ under GRH, in terms of standard invariants of $K$ and each $A_i$, where $c(A)$ is defined to be the smallest positive integer such that for any prime $\ell>c(A)$, the image of the $\ell$-adic Galois representation of $A$ is "as large as possible" in a suitable sense.
