Shranjeno v:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Izdano: |
2020
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/2012.01337 |
| Oznake: |
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Kazalo:
- 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 $A/K$.