Singular moduli and supersingular moduli of Drinfeld modules

DOI10.1007/BF01231341zbMath0767.11028OpenAlexW2092230331MaRDI QIDQ1209143

Martin L. Brown

Publication date: 16 May 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144059

zbMATH Keywords

Carlitz modulemodular formsDrinfeld modulesChebotarev density theoremquadratic reciprocity\(q\)-expansionssupersingular reductionrank 2 Drinfeld modulesexceptional \(j\)-invariant

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Families, moduli of curves (algebraic) (14H10) Complex multiplication and moduli of abelian varieties (11G15) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items (10)

Height and torsion of rank-2 Drinfield modules ⋮ Supersingular reduction of Drinfel'd modules ⋮ The Mumford-Tate conjecture for Drinfeld-modules ⋮ A transcendence theorem in finite characteristic. ⋮ Zeros of certain Drinfeld modular functions ⋮ Frobenius distributions of Drinfeld modules of any rank ⋮ On class number relations over function fields ⋮ On singular moduli of Drinfeld modules in characteristic two ⋮ On the coefficients of modular polynomials for Drinfeld modules ⋮ The André-Oort conjecture for the product of two Drinfeld modular curves.

Cites Work

• Zur Arithmetik von Drinfeld-Moduln
• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• On the coefficients of Drinfeld modular forms
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Algebraic Groups Over Finite Fields
• Note On Supersingular Primes of Elliptic Curves Over Q
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