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Root numbers of abelian varieties

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Matthew Bisatt
King's College London/MPIM
Mit, 2018-12-12 14:30 - 15:30
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Given an abelian variety over a global field, one of its most interesting invariants is its rank. This is notoriously difficult to compute, so instead we simply ask: is the rank is odd or even? The answer to this is (conjecturally) encoded in the corresponding root number.

I will explore what information one needs to compute a root number and how to extract this data for hyperelliptic curves. As an application, we will produce an example such that every quadratic twist should have positive rank.

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