Comparison of different Tate conjectures

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Veronika Ertl
  • Timo Keller
  • Yanshuai Qin

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OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 24 Juni 2024

Abstract

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 $A/K$.

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Comparison of different Tate conjectures. / Ertl, Veronika; Keller, Timo; Qin, Yanshuai.
2024.

Publikation: Arbeitspapier/Preprint › Preprint

Ertl, V., Keller, T., & Qin, Y. (2024). Comparison of different Tate conjectures. Vorabveröffentlichung online. https://doi.org/10.48550/arXiv.2012.01337
Ertl V, Keller T, Qin Y. Comparison of different Tate conjectures. 2024 Jun 24. Epub 2024 Jun 24. doi: 10.48550/arXiv.2012.01337
Ertl, Veronika ; Keller, Timo ; Qin, Yanshuai. / Comparison of different Tate conjectures. 2024.
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