论文标题
比较不同的泰特猜想
Comparison of different Tate conjectures
论文作者
论文摘要
对于Abelian品种$ a $，超过有限生成的字段$ k $的特征$ p> 0 $，我们证明代数排名$ a $最多是适当定义的分析等级。 Moreover, we prove that equality, i.e., the BSD rank conjecture, holds for $A/K$ if and only if a suitably defined Tate--Shafarevich group of $A/K$ (1) has finite $\ell$-primary component for some/all $\ell \neq p$, or (2) finite prime-to-$p$ part, or (3) has $p$-primary part of finite指数或（4）为有限指数。有一种算法可以验证$ a/k $的具体情况。
For an abelian variety $A$ over a finitely generated field $K$ of characteristic $p > 0$, we prove that the algebraic rank of $A$ is at most a suitably defined analytic rank. Moreover, we prove that equality, i.e., the BSD rank conjecture, holds for $A/K$ if and only if a suitably defined Tate--Shafarevich group of $A/K$ (1) has finite $\ell$-primary component for some/all $\ell \neq p$, or (2) finite prime-to-$p$ part, or (3) has $p$-primary part of finite exponent, or (4) is of finite exponent. There is an algorithm to verify those conditions for concretely given $A/K$.
