Moduli for rational genus 2 curves with real multiplication for discriminant 5

DOI10.5802/jtnb.1286MaRDI QIDQ6642858

Alex Cowan, Kimball Martin

Publication date: 25 November 2024

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

zbMATH Keywords

Hilbert modular surfacesgenus 2 curvesreal multiplicationsmaster conics

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Abelian varieties of dimension (> 1) (11G10) Quadratic forms over global rings and fields (11E12) Algebraic moduli of abelian varieties, classification (14K10) [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)] Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Cites Work

• K3 surfaces and equations for Hilbert modular surfaces
• Serre's modularity conjecture. I
• The Magma algebra system. I: The user language
• General form of Humbert's modular equation for curves with real multiplication of \(\Delta =5\)
• Real multiplication through explicit correspondences
• Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
• Rigorous computation of the endomorphism ring of a Jacobian
• Abelian varieties over Q and modular forms
• Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19
• On Brumer's family of RM-curves of genus two
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