Geodesic
On the Average Number of 2-Selmer Elements of Elliptic Curves over $\mathbb F_q(X)$ with Two Marked Points
Documenta mathematica, Tome 24 (2019), pp. 1179-1223
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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 G-torsors over an algebraic curve, where G is isogenous to SL24​, and show that the images of 2-Selmer elements under this map become equidistributed in the limit.
DOI : 10.4171/dm/702
Classification : 11G05, 14H60
Mots-clés : elliptic curves, Selmer groups, rational points 
@article{10_4171_dm_702,
     author = {Jack A. Thorne},
     title = {On the {Average} {Number} of {2-Selmer} {Elements} of {Elliptic} {Curves} over $\mathbb F_q(X)$ with {Two} {Marked} {Points}},
     journal = {Documenta mathematica},
     pages = {1179--1223},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/702},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/702/}
}
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Jack A. Thorne. On the Average Number of 2-Selmer Elements of Elliptic Curves over $\mathbb F_q(X)$ with Two Marked Points. Documenta mathematica, Tome 24 (2019), pp. 1179-1223. doi: 10.4171/dm/702

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