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

Toshiro Hiranouchi

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arXiv · 2504.05595

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

Toshiro Hiranouchi

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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.

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Toshiro Hiranouchi. 2025-04-08. A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields. https://arxiv.org/abs/2504.05595

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