On the computation of Tamagawa numbers and Neron component groups of Jacobians of semistable hyperelliptic curves.
We describe an algorithm for calculating Tamagawa numbers of Jacobians of semistable hyperelliptic curves over local fields in terms of their reduction types. The computation is uniform across combinatorial families of reduction types, and thereby yields a finite algorithm to produce explicit characterisations of these Tamagawa numbers for all such curves of a fixed genus. As a corollary to the theory we develop, we derive new restrictions on the behaviour of these Tamagawa numbers as the base field is varied.
Publisher URL: http://arxiv.org/abs/1808.05479
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