An Asymptotic formula for Tate-Shafarevich groups of CM elliptic curves at supersingular primes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912316105162752 |
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| author | Müller, Katharina |
| author_facet | Müller, Katharina |
| contents | Let $K$ be an imaginary quadratic field and $E/\mathbb{Q}$ an elliptic curves with complex multiplication by $\mathcal{O}_K$. Let $K_\infty/K$ be the anticyclotomic $\mathbb{Z}_p$-extension of $K$ and $K_n$ the intermediate layers. Under additional assumptions on Kobayashi's signed Selmer groups we prove an asymptotic formula for the Tate-Shafarevich group over $K_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Asymptotic formula for Tate-Shafarevich groups of CM elliptic curves at supersingular primes Müller, Katharina Number Theory 11r23, 11G05, 11G15 Let $K$ be an imaginary quadratic field and $E/\mathbb{Q}$ an elliptic curves with complex multiplication by $\mathcal{O}_K$. Let $K_\infty/K$ be the anticyclotomic $\mathbb{Z}_p$-extension of $K$ and $K_n$ the intermediate layers. Under additional assumptions on Kobayashi's signed Selmer groups we prove an asymptotic formula for the Tate-Shafarevich group over $K_n$. |
| title | An Asymptotic formula for Tate-Shafarevich groups of CM elliptic curves at supersingular primes |
| topic | Number Theory 11r23, 11G05, 11G15 |
| url | https://arxiv.org/abs/2504.05734 |