A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields

Toshiro Hiranouchi

A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields

Number Theory 2025-04-09 v1 Algebraic Geometry

Authors: Toshiro Hiranouchi

Abstract

We investigate the higher Chow groups, specifically $SK_1(E)$ for elliptic curves $E$ over number fields $F$ . Focusing on the kernel $V(E)$ of the norm map $SK_1(E)\to F^{\times}$ , we analyze its mod $p$ structure. We provide conditions, based on the mod $p$ Galois representations associated to $E$ , under which the torsion subgroup of $V(E)$ is infinite.

Keywords

Hasse principle GL2(Fp) Bloch exact sequence elliptic curves number fields higher Chow groups SK1 mod p Galois representations

Cite

@article{arxiv.2504.05595,
  title  = {A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields},
  author = {Toshiro Hiranouchi},
  journal= {arXiv preprint arXiv:2504.05595},
  year   = {2025}
}

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