Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 and PSO2n+2 on self-adjoint operators and show how they facilitate in computing the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational Weierstrass point, and the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational non-Weierstrass point, over arbitrary number fields. / Mathematics
| Identifer | oai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/11156784 |
| Date | 08 October 2013 |
| Creators | Wang, Xiaoheng |
| Contributors | Gross, Benedict H. |
| Publisher | Harvard University |
| Source Sets | Harvard University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Rights | open |
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