On distribution of supersingular primes of abelian varieties and K3 surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909609954902016 |
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| author | Hui, Chun-Yin |
| author_facet | Hui, Chun-Yin |
| contents | Let X be an abelian variety or a K3 surface defined over a number field K. We prove that the density of the supersingular primes of X is zero if X is non-CM. By applying an effective Chebotarev density theorem of Serre, we obtain asymptotic upper bounds of the counting function for these supersingular primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On distribution of supersingular primes of abelian varieties and K3 surfaces Hui, Chun-Yin Number Theory Algebraic Geometry Let X be an abelian variety or a K3 surface defined over a number field K. We prove that the density of the supersingular primes of X is zero if X is non-CM. By applying an effective Chebotarev density theorem of Serre, we obtain asymptotic upper bounds of the counting function for these supersingular primes. |
| title | On distribution of supersingular primes of abelian varieties and K3 surfaces |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2504.08088 |