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Reduction Types of Genus 2 Curves
Edwina Aylward, Lilybelle Cowland Kellock, Vladimir Dokchitser +1
Tate produced a table for elliptic curves over local fields that beautifully summarises their arithmetic invariants in terms of the Kodaira type. We present an analogous set of tab…
Invariants recovering the reduction type of a hyperelliptic curve
Lilybelle Cowland Kellock, Elisa Lorenzo
Tate's algorithm tells us that for an elliptic curve over a local field of residue characteristic , has potentially good reduction if and only if $\text{ord}(…
Root numbers and parity phenomena
Lilybelle Cowland Kellock, Vladimir Dokchitser
The parity conjecture has a long and distinguished history. It gives a way of predicting the existence of points of infinite order on elliptic curves without having to construct th…