The isogeny class of a CM-type abelian variety is defined over a finite extension of the prime field

DOI10.1016/0022-4049(73)90040-6zbMath0272.14009OpenAlexW2016309685MaRDI QIDQ759072

Frans Oort

Publication date: 1973

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(73)90040-6

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Arithmetic ground fields for abelian varieties (14K15) Complex multiplication and abelian varieties (14K22)

Related Items

On the number of connected components of real abelian varieties that admit sufficiently many complex multiplications, Endomorphism algebras of QM abelian surfaces, Non-isogenous superelliptic Jacobians, Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli, A note on supersingular abelian varieties, Simple complex tori of algebraic dimension 0, The isomorphism classes of abelian varieties of CM-type., Abelian varieties over finite fields as basic abelian varieties, Abelian varieties over fields of finite characteristic, Non-communtative Iwasawa main conjecture, Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure, On reduction of moduli schemes of abelian varieties with definite quaternion multiplications, Subvarieties of moduli spaces

Cites Work

• Endomorphisms of Abelian varieties over finite fields
• Good reduction of abelian varieties
• Commutative group schemes
• Good and stable reduction of Abelian varieties
• Rational Points of Abelian Varieties Over Function Fields
• THE THEORY OF COMMUTATIVE FORMAL GROUPS OVER FIELDS OF FINITE CHARACTERISTIC
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