Supersingular Genus-two Curves over Fields of Characteristic Three
نویسندگان
چکیده
Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y = x + 1 then up to isomorphism there are exactly 20 degree-3 maps φ from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C, E, φ), paying particular attention to questions of rationality. The results we obtain allow us to determine, for every finite field k of characteristic 3, the polynomials that occur as Weil polynomials of supersingular genus-2 curves over k.
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