The 2-parity conjecture for Jacobians of hyperelliptic curves

Adam Morgan (University of Glasgow)

Wednesday 20th October 16:00-17:00 Maths 110

Abstract

For an abelian variety A defined over a number field, the parity conjecture asserts that the global root number of A determines the parity of its rank.
Since the former is much easier to compute, this has several important implications for the arithmetic of A.
After reviewing some of these I will discuss progress towards a variant of this, the 2-parity conjecture, for Jacobians of hyperelliptic curves.
Part of this is joint with Vladimir Dokchitser and Holly Green.

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