On the Average Number of 2-Selmer Elements of Elliptic Curves over with Two Marked Points
Jack A. ThorneDepartment of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
We consider elliptic curves over global fields of positive characteristic with two distinct marked non-trivial rational points. Restricting to a certain subfamily of the universal one, we show that the average size of the 2-Selmer groups of these curves exists, in a natural sense, and equals 12. Along the way, we consider a map from these 2-Selmer groups to the moduli space of -torsors over an algebraic curve, where is isogenous to , and show that the images of 2-Selmer elements under this map become equidistributed in the limit.
Cite this article
Jack A. Thorne, On the Average Number of 2-Selmer Elements of Elliptic Curves over with Two Marked Points. Doc. Math. 24 (2019), pp. 1179–1223DOI 10.4171/DM/702