The average rank of elliptic $n$-folds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2010
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| _version_ | 1866909353600090112 |
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| author | Kloosterman, Remke |
| author_facet | Kloosterman, Remke |
| contents | Let $V/\mathbb{F}_q$ be a variety of dimension at least two. We show that the density of elliptic curves $E/\mathbb{F}_q(V)$ with positive rank is zero if $V$ has dimension at least 3 and is at most $1-ζ_V(3)^{-1}$ if $V$ is a surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1010_0152 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | The average rank of elliptic $n$-folds Kloosterman, Remke Number Theory Algebraic Geometry Let $V/\mathbb{F}_q$ be a variety of dimension at least two. We show that the density of elliptic curves $E/\mathbb{F}_q(V)$ with positive rank is zero if $V$ has dimension at least 3 and is at most $1-ζ_V(3)^{-1}$ if $V$ is a surface. |
| title | The average rank of elliptic $n$-folds |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/1010.0152 |