论文标题
Artin对弗罗贝尼乌斯条件的阿贝利亚品种的猜想
Artin's Conjecture for Abelian Varieties with Frobenius Condition
论文作者
论文摘要
$ a $是一个数字字段$ k $ dimension $ r $，$ a_1，\ dots，a_g \ a（k）$和$ f/k $ a有限的galois扩展名的$ a $。我们考虑$ k $的总理$ \ frak p $的密度，使得商$ \ bar {a}（k（{\ frak p}））/\ langle \ bar {a} _1，\ dots，\ bar {a} _g \ rangle $ y ange $ 2r-$ $ 2r-c的$ 2 $ $ cyiip and $ cyii fraus and $ cycon fraus frous frous frous fraus frous fr。尊重$ f/k $，其中$ \ bar {a} $是$ a $ a $ a $ modulo $ \ frak p $，$ k（\ frak p）$是$ \ frak p $和$ \ frak p $和$ \ langle \ langle \ bar {a} _1 _1，\ bar \ bar \ bar \ bar {a} a}的残留类字段$ \ bar {a} _1，\ dots，\ bar {a} _g $。我们开发了一个一般框架，以证明普遍的Riemann假设下的密度存在。
$A$ be an abelian variety over a number field $K$ of dimension $r$, $a_1, \dots, a_g \in A(K)$ and $F/K$ a finite Galois extension. We consider the density of primes $\frak p$ of $K$ such that the quotient $\bar{A}(k({\frak p}))/\langle \bar{a}_1,\dots,\bar{a}_g\rangle$ has at most $2r-1$ cyclic components and $\frak p$ satisfies a Frobenius condition with respect to $F/K$, where $\bar{A}$ is the reduction of $A$ modulo $\frak p$, $k(\frak p)$ is the residue class field of $\frak p$ and $\langle \bar{a}_1,\dots,\bar{a}_g\rangle$ is the subgroup generated by the reductions $\bar{a}_1,\dots,\bar{a}_g$. We develop a general framework to prove the existence of the density under the Generalized Riemann Hypothesis.
