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If $X$ is a smooth, geometrically connected, projective curve of genus $g$ over $\mathbb{F}_q$, then the zeta function of $X$ is of the form $P(s)/(1 - s)(1 - qs)$, where $P(s)$ is a polynomial of ...

If $p$ is a prime, $n\in\mathbb{N}$ is a natural number and $C$ is a nonsingular curve over $\mathbb{F}_{p^{n}}$, the $\zeta$ function associated to $C\mid_{\mathbb{F}_{p^{n}}}$ is defined as \begin{...

There is an isomorphism between (rational) correspondences on a curve $C/\mathbb{F}_p$ orthogonal to the "valence zero" ones (i.e. orthogonal under intersection pairing to $\{*\}\times C$ and $C\times ...