2‐Selmer parity for hyperelliptic curves in quadratic extensions

DOI10.1112/plms.12565arXiv1504.01960OpenAlexW2230328840MaRDI QIDQ6139776

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Publication date: 19 December 2023

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01960

zbMATH Keywords

hyperelliptic curves2-parity conjecture

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Curves over finite and local fields (11G20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic ground fields for abelian varieties (14K15)

Cites Work

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• The \(p\)-parity conjecture for elliptic curves with a \(p\)-isogeny
• Disparity in Selmer ranks of quadratic twists of elliptic curves
• Some consequences of a formula of Mazur and Rubin for arithmetic local constants
• Torsion and Tamagawa numbers
• On quadratic twists of hyperelliptic curves
• The norm map for ordinary Abelian varieties
• The Schur index in the theory of group representation
• Regulator constants and the parity conjecture
• On the Birch-Swinnerton-Dyer quotients modulo squares
• There are no abelian varieties over \(\mathbb Z\).
• Rational points of the group of components of a Néron model
• Class groups and Selmer groups
• The Cassels-Tate pairing on polarized Abelian varieties
• Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
• Twisting commutative algebraic groups
• Self cup products and the theta characteristic torsor
• Quadratic twists of abelian varieties and disparity in Selmer ranks
• Finding large Selmer rank via an arithmetic theory of local constants
• Curves in characteristic \(2\) with non-trivial \(2\)-torsion
• On pencils of curves of genus two
• Duality theorems for curves over p-adic fields
• Rational points of Abelian varieties with values in towers of number fields
• The complete classification of fibres in pencils of curves of genus two
• Arithmetic of hyperelliptic curves over local fields
• Root numbers and parity of ranks of elliptic curves
• Random maximal isotropic subspaces and Selmer groups
• Root numbers of abelian varieties
• Root numbers, Selmer groups, and non-commutative Iwasawa theory
• Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète
• Arithmetic of Elliptic Curves Upon Quadratic Extension
• Néron Models
• Modèles minimaux des courbes de genre deux.
• The ℓ-parity conjecture over the constant quadratic extension
• Models of hyperelliptic curves with tame potentially semistable reduction
• The remaining cases of the Kramer–Tunnell conjecture
• Theta characteristics of an algebraic curve
• Modeles de neron et monodromie
• Variation of Tamagawa numbers of semistable abelian varieties in field extensions
• On the arithmetic of abelian varieties
• Two-torsion of the Jacobian of hyperelliptic curves over finite fields
• On the parity conjecture for abelian surfaces
• A user's guide to the local arithmetic of hyperelliptic curves

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