Genus two curves with full \(\sqrt{3}\)-level structure and Tate-Shafarevich groups

DOI10.1007/s00029-023-00839-wzbMath1528.11055arXiv2102.04319OpenAlexW3127020250WikidataQ122178684 ScholiaQ122178684MaRDI QIDQ6103430

Ari Shnidman, E. Victor Flynn, Nils Bruin

Publication date: 5 June 2023

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.04319

zbMATH Keywords

Tate-Shafarevich groupJacobianshigher genus curves

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) [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)]

Cites Work

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• K3 surfaces and equations for Hilbert modular surfaces
• Courbes sur une variété abélienne et points de torsion
• The Magma algebra system. I: The user language
• Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families
• On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes
• \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
• Canonical heights on genus-2 Jacobians
• The complete classification of fibres in pencils of curves of genus two
• Arithmetic of hyperelliptic curves over local fields
• The Arithmetic of Genus Two Curves with (4,4)-Split Jacobians
• Descent via (3,3)-isogeny on Jacobians of genus 2 curves
• Heuristics on class groups and on Tate-Shafarevich groups
• Néron Models
• On Ribet’s isogeny for $J_0(65)$
• Arithmetic aspects of the Burkhardt quartic threefold
• Abelian surfaces of GL₂-type as Jacobians of curves
• Quadratic Twists of Abelian Varieties With Real Multiplication
• Multivariate normal distribution for integral points on varieties
• Local invariants of isogenous elliptic curves
• An effective Chabauty–Kim theorem

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