Tate classes on self-products of Abelian varieties over finite fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909354614063104 |
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| author | Zarhin, Yuri G. |
| author_facet | Zarhin, Yuri G. |
| contents | We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_04478 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Tate classes on self-products of Abelian varieties over finite fields Zarhin, Yuri G. Algebraic Geometry Number Theory 11G10, 11G25, 14G15 We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya. |
| title | Tate classes on self-products of Abelian varieties over finite fields |
| topic | Algebraic Geometry Number Theory 11G10, 11G25, 14G15 |
| url | https://arxiv.org/abs/2005.04478 |