A Hasse principle for GL₂(\mathbbF_p) and Bloch's exact sequence for elliptic curves over number fields

2025/04/08 by Toshiro Hiranouchi, Hiranouchi, Toshiro
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2504.05595

Abstract

We investigate the higher Chow groups, specifically SK₁(E) for elliptic curves E over number fields F. Focusing on the kernel V(E) of the norm map SK₁(E)→ F^×, 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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