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    $\begingroup$ Please use high-level tags like ag.algebraic-geometry and nt.number-theory. I added these tags now. Regarding high-level tags, see meta.mathoverflow.net/q/1075 $\endgroup$ Commented 11 hours ago
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    $\begingroup$ The case of hypersurfaces, in particular plane curves, is done in Chapter V of Koblitz's "p-adic Numbers, p-adic Analysis, and Zeta-Functions", Springer, 1984. $\endgroup$ Commented 9 hours ago