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arXiv · 1310.5026

On Tate's conjecture for elliptic modular surfaces over finite fields

Rémi Lodh
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Abstract

For $N\geq 3$, we show Tate's conjecture for the elliptic modular surface $E(N)$ of level $N$ over $\mathbb{F}_p$ for a prime $p$ satisfying $p\equiv 1\mod N$ outside of a set of primes of density zero. We also prove a strong form of Tate's conjecture for $E(N)$ over any finite field of characteristic $p$ prime to $N$ under the assumption that the formal Brauer group of $E(N)$ is of finite height.

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Rémi Lodh. 2013-11-22. On Tate's conjecture for elliptic modular surfaces over finite fields. https://arxiv.org/abs/1310.5026

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