Arithmetic aspects of the Burkhardt quartic threefold

DOI10.1112/jlms.12153zbMath1446.11111arXiv1705.09006OpenAlexW3122927433MaRDI QIDQ4646244

Brett Nasserden, Nils Bruin

Publication date: 11 January 2019

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

Full work available at URL: https://arxiv.org/abs/1705.09006

zbMATH Keywords

Burkhardt quartic threefoldHesse pencil

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Abelian varieties of dimension (> 1) (11G10) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Algebraic moduli of abelian varieties, classification (14K10) Arithmetic aspects of modular and Shimura varieties (11G18) [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)]

Related Items (6)

Genus two curves with full \(\sqrt{3}\)-level structure and Tate-Shafarevich groups ⋮ \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field ⋮ Abelian surfaces over totally real fields are potentially modular ⋮ Twists of the Burkhardt quartic threefold ⋮ Abelian surfaces with fixed 3-torsion ⋮ Rationality of twists of the Siegel modular variety of genus 2 and level 3

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