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
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917980552560640 |
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| author | Hiranouchi, Toshiro |
| author_facet | Hiranouchi, Toshiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields Hiranouchi, Toshiro Number Theory Algebraic Geometry 11G05, 14C15, 19D45 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. |
| title | A Hasse principle for $GL_2(\mathbb{F}_p)$ and Bloch's exact sequence for elliptic curves over number fields |
| topic | Number Theory Algebraic Geometry 11G05, 14C15, 19D45 |
| url | https://arxiv.org/abs/2504.05595 |