Average Ranks of Elliptic Curves after p-Extension

Ross Paterson (University of Glasgow)

Wednesday 1st December, 2021 16:00-17:00 Maths 110


As E varies among elliptic curves defined over the rational numbers, a theorem of Bhargava and Shankar shows that the average rank of the group of rational points on E is bounded.  If we now fix a number field K, is the same true of the K-points?  I will report on recent progress on this question, answering in the affirmative for certain choices of K.

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