On a Question of Zannier
نویسنده
چکیده
We fix an integer N ≥ 1 and an elliptic curve E over Z[1/6N ], given by an equation y = f(x) with f(x) a cubic in Z[1/6N ] whose discriminant is invertible in Z[1/6N ]. On E we have the differential of the first kind ω = dx/y and the differential of the second kind η = xdx/y. For each prime p not dividing 6N , we look at this data mod p, and apply the Cartier operator Cp. We get quantities αp, βp ∈ Fp defined by Cp(ω) = αpω, Cp(η) = βpω.
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