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

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arxiv 2504.05595 v1 pith:FZV25VAV submitted 2025-04-08 math.NT math.AG

Toshiro Hiranouchi This is my paper · ORCID

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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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A Hasse principle for the higher Chow groups of curves over a global field
math.NT 2025-07 reject novelty 6.0 of 10

For smooth projective curves over global fields, the mod-l kernel of the boundary map is governed by local reduction data and the Galois coinvariants J[l]_{G_F}.

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