On the nonexistence of certain curves of genus two

dc.creatorHowe, Everett W.
dc.date2002-01-31
dc.date.accessioned2026-07-07T04:46:13Z
dc.date.available2026-07-07T04:46:13Z
dc.descriptionWe prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our proof uses the Brauer relations in a biquadratic extension of Q to show that every principally polarized abelian surface over F_q with the given characteristic polynomial splits over F_{q^2} as a product of polarized elliptic curves.
dc.descriptionLaTeX, 13 pages
dc.identifierhttps://arxiv.org/abs/math/0201311
dc.identifierhttp://arxiv.org/abs/math/0201311
dc.identifierCompos. Math. 140 (2004) 581--592
dc.identifierdoi:10.1112/S0010437X03000757
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63243
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G20 (Primary); 11G10, 11R65, 14G15, 14H25 (Secondary)
dc.titleOn the nonexistence of certain curves of genus two
dc.typetext

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