Quadratic forms and genus theory: a link with 2-descent and an application to nontrivial specializations of ideal classes

DOI10.1112/JLMS.12921MaRDI QIDQ6561004

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Publication date: 24 June 2024

Published in: Journal of the London Mathematical Society. Second Series (Search for Journal in Brave)

zbMATH Keywords

principal ideal domaingenus theoryideal classes

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Jacobians, Prym varieties (14H40) Density theorems (11R45) General binary quadratic forms (11E16)

Cites Work

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• Pulling back torsion line bundles to ideal classes
• Gauss composition over an arbitrary base
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• Composition of binary quadratic forms
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• Cycles of quadratic polynomials and rational points on a genus-2 curve
• 2-descent on the Jacobians of hyperelliptic curves
• TRIVIALITY OF VECTOR BUNDLES OVER THE AFFINE SPACE K ²
• From Picard groups of hyperelliptic curves to class groups of quadratic fields
• Computing in the Jacobian of a Hyperelliptic Curve
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• Line bundles, rational points and ideal classes

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