### Computation of p-adic heights in families of elliptic curves

Linfoot Number Theory Seminar

30th May 2018, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

Given an elliptic curve E over Q and a prime p of good ordinary reduction, there is a natural p-adic analogue of the real canonical height on E. The discriminant of the induced pairing on the free part of the Mordell-Weil group appears in p-adic BSD. However, unlike in the real case, this quantity is only conjectured to be non-zero. I will present a new algorithm to compute p-adic heights in families of elliptic curves, with applications to non-degeneracy. The algorithm uses a modified version of Lauder's deformation method for the computation of the action of Frobenius on an appropriate cohomology group.

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