A Hasse principle of the higher chow groups for an elliptic curve over a global function field

Toshiro Hiranouchi

A Hasse principle of the higher chow groups for an elliptic curve over a global function field

Number Theory 2025-08-25 v2

Authors: Toshiro Hiranouchi

Abstract

We investigate the structure of the higher Chow groups $CH^2(E,1)$ for an elliptic curve $E$ over a global function field $F$ . Focusing on the kernel $V(E)$ of the push-forward map $CH^2(E,1)\to F^{\times}$ associated to the structure map $E\to \operatorname{Spec}(F)$ , we analyze the torsion part $V(E)$ based on the mod $l$ Galois representations associated to the $l$ -torsion points $E[l]$ .

Keywords

Hasse principle higher Chow groups elliptic curve global function field torsion

Cite

@article{arxiv.2507.22319,
  title  = {A Hasse principle of the higher chow groups for an elliptic curve over a global function field},
  author = {Toshiro Hiranouchi},
  journal= {arXiv preprint arXiv:2507.22319},
  year   = {2025}
}

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