### Local root and Tamagawa numbers of hyperelliptic curves

Linfoot Number Theory Seminar

19th May 2021, 11:00 am – 12:00 pm

Fry Building, Online

Given a p-adic field K we consider a hyperelliptic curve of genus (p-1)/2 defined over K. Under the hypothesis that the associated l-adic Galois representation is wildly ramified, we give a formula for the number of rational components of the Néron model of the Jacobian, generalizing Tate's algorithm. As an application for genera 1 and 2, we assume further that the Galois representation has the maximal possible inertia image and give geometric formulae for the root numbers.

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