On the existence of abelian surfaces with everywhere good reduction

DOI10.1090/mcom/3692zbMath1493.11098arXiv1903.10394OpenAlexW2924186347MaRDI QIDQ5070545

Lassina Dembélé

Publication date: 13 April 2022

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.10394

zbMATH Keywords

abelian varietiesHilbert modular forms

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Uses Software

• Magma

Cites Work

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• Examples of abelian surfaces with everywhere good reduction
• K3 surfaces and equations for Hilbert modular surfaces
• Serre's conjecture over \(\mathbb F_9\)
• Finiteness theorems for abelian varieties over number fields.
• There are no abelian varieties over \(\mathbb Z\).
• On p-adic Hecke algebras for \(GL_ 2\) over totally real fields
• 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
• Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields
• Abelian varieties over cyclotomic fields with good reduction everywhere
• An automorphic generalization of the Hermite-Minkowski theorem
• Automorphy of some residually \(S_5\) Galois representations
• Elliptic curves over real quadratic fields are modular
• A database of number fields
• The Arithmetic of Genus Two Curves with (4,4)-Split Jacobians
• Computing Genus-2 Hilbert–Siegel Modular Forms over via the Jacquet–Langlands Correspondence
• The Arithmetic of Elliptic Curves
• Modular symbols for ₁(N) and elliptic curves with everywhere good reduction
• Mod 2 and mod 5 icosahedral representations
• Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
• Determination of elliptic curves with everywhere good reduction over real quadratic fields Q(\sqrt3p)
• Abelian surfaces of GL₂-type as Jacobians of curves
• Explicit Methods for Hilbert Modular Forms
• Computing algebraic numbers of bounded height