Examples of abelian surfaces with everywhere good reduction

DOI10.1007/s00208-015-1252-6zbMath1410.11059arXiv1309.3821OpenAlexW3103140817MaRDI QIDQ261442

Lassina Dembélé, Abhinav Kumar

Publication date: 23 March 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3821

zbMATH Keywords

good reductionHilbert modular formsEichler-Shimura conjectureparamodular level structures

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items

Computing points of bounded height in projective space over a number field, On the existence of abelian surfaces with everywhere good reduction, Theta lifts of Bianchi modular forms and applications to paramodularity, Some extensions of the modular method and Fermat equations of signature \((13,13,n)\), Periods of Modular GL₂-type Abelian Varieties and p-adic Integration, Quadratic \(\mathbb Q\)-curves, units and Hecke \(L\)-values, On the paramodularity of typical abelian surfaces, Abelian surfaces over totally real fields are potentially modular

Uses Software

• Magma
• SageMath
• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• K3 surfaces and equations for Hilbert modular surfaces
• Siegel modular forms of degree two attached to Hilbert modular forms
• Class fields of abelian extensions of \(\mathbb Q\)
• Elliptic curves with trivial conductor over quadratic fields
• Serre's conjecture over \(\mathbb F_9\)
• A modularity lifting theorem for weight two Hilbert modular forms
• There are no abelian varieties over \(\mathbb Z\).
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Elliptic curves with good reduction everywhere over quadratic fields and having rational \(j\)-invariant
• Reduction of elliptic curves over imaginary quadratic number fields
• The special values of the zeta functions associated with Hilbert modular forms
• Stable genus 2 curves and their moduli scheme
• The Magma algebra system. I: The user language
• Residually reducible representations and modular forms
• Jacobian nullwerte and algebraic equations
• On Serre's reciprocity conjecture for 2-dimensional mod \(p\) representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\)
• On abelian varieties with many endomorphisms and a conjecture of Shimura's
• Galois properties of points of finite order of elliptic curves
• Class fields over real quadratic fields and Hecke operators
• On the factors of the Jacobian variety of a modular function field
• Examples of CM curves of genus two defined over the reflex field
• Computational Aspects of Modular Forms and Galois Representations
• Hilbert Modular Forms and Their Applications
• Artin’s conjecture for representations of octahedral type
• Modular symbols for ₁(N) and elliptic curves with everywhere good reduction
• S -Unit Equations, Binary Forms and Curves of Genus 2
• Determination of elliptic curves with everywhere good reduction over ℚ(√37)
• Abelian surfaces of GL₂-type as Jacobians of curves
• Elliptic curves with good reduction away from 2: II
• Explicit Methods for Hilbert Modular Forms
• Computing Hilbert Modular Forms over Fields with Nontrivial Class Group
• Paramodular abelian varieties of odd conductor
• Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes
• Computing algebraic numbers of bounded height
• Periods of Hilbert modular surfaces
• Heights of Heegner points on Shimura curves.