E 8 and the average size of the 3‐Selmer group of the Jacobian of a pointed genus‐2 curve
Published version
Peer-reviewed
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Repository DOI
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Authors
Romano, Beth
Thorne, Jack A.
Abstract
Abstract: We prove that the average size of the 3‐Selmer group of a genus‐2 curve with a marked Weierstrass point is 4. We accomplish this by studying rational and integral orbits in the representation associated to a stably Z / 3 Z ‐graded simple Lie algebra of type E 8 . We give new techniques to construct integral orbits, inspired by the proof of the fundamental lemma and by the twisted vertex operator realisation of affine Kac–Moody algebras.
Description
Keywords
Research Article, Research Articles, 14G05 (primary)
Journal Title
Proceedings of the London Mathematical Society
Conference Name
Journal ISSN
0024-6115
1460-244X
1460-244X
Volume Title
122
Publisher
Publisher DOI
Sponsorship
EPSRC (EP/N007204/1)
European Research Council (714405)
European Research Council (714405)