2018/08/16 by L. Alexander Betts, Betts, L. Alexander
Mathematics · #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1808.05479
We study how Tamagawa numbers of Jacobians of hyperelliptic curves vary as\none varies the base field or the curve, in the case of semistable reduction. We\nfind that there are strong constraints on the behaviour that appears, some of\nwhich are unexpected and specific to hyperelliptic curves. Our methods are\nexplicit and allow one to write down formulae for Tamagawa numbers of infinite\nfamilies of hyperelliptic curves, of the kind used in proofs of the parity\nconjecture for Jacobians of curves of small genus.\n