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Properties of R
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Classroom Contents
2-Selmer Groups, 2-Class Groups, and the Arithmetic of Binary Forms
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- 1 Intro
- 2 Roadmap
- 3 The Definition of R
- 4 Properties of R
- 5 Fractional Ideals of R
- 6 A Theorem of Hecke
- 7 Questions
- 8 Orbit Parametrization
- 9 Construction of An Integral Orbit
- 10 Image of the Parametrization
- 11 Primer on Parametrize-and-Count Strategy
- 12 2-Torsion in the Class Group of R
- 13 Integral Solutions to Superelliptic Equations (cont'd.)
- 14 2-Selmer Groups of Hyperelliptic Jacobians (cont'd.)
- 15 Varying the Leading Coefficient (cont'd.)
- 16 Error from Davenport's Lemma (cont'd.)
- 17 2-Selmer Groups of Genus-1 Curves
- 18 Background on Elliptic Curves and their Selmer groups
- 19 Progress toward the Conjecture
- 20 The Second Moment
- 21 Class Group Application
