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In mathematics, the Honda–Tate theorem classifies abelian varieties over finite fields up to isogeny. It states that the isogeny classes of simple abelian varieties over a finite field of order q correspond to algebraic integers all of whose conjugates (given by eigenvalues of the Frobenius endomorphism on the first cohomology group or Tate module) have absolute value √q. Tate showed that the map taking an isogeny class to the eigenvalues of the Frobenius is injective, and Taira Honda showed that this map is surjective, and therefore a bijection.

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  • Honda–Tate theorem (en)
  • Honda–Tates sats (sv)
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  • In mathematics, the Honda–Tate theorem classifies abelian varieties over finite fields up to isogeny. It states that the isogeny classes of simple abelian varieties over a finite field of order q correspond to algebraic integers all of whose conjugates (given by eigenvalues of the Frobenius endomorphism on the first cohomology group or Tate module) have absolute value √q. Tate showed that the map taking an isogeny class to the eigenvalues of the Frobenius is injective, and Taira Honda showed that this map is surjective, and therefore a bijection. (en)
  • Inom matematiken är Honda–Tates sats ett resultat som klassificerar abelska varieteter över ändliga kroppar upp till . Satsen säger att isogeniklasserna av enkla abelska varieteter över en ändlig kropp av ordning q korresponderar till algebraiska heltal vars alla konjugat (som ges av egenvärdena av av första kohomologigruppen eller ) har absolut värde √q. bevisade att avbildningen som tar isogeniklassen till egenvärdena av Frobeniusendomorfin är injektiv, och bevisade att den är surjektiv, och härmed en bijektion. (sv)
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  • Taira Honda (en)
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  • In mathematics, the Honda–Tate theorem classifies abelian varieties over finite fields up to isogeny. It states that the isogeny classes of simple abelian varieties over a finite field of order q correspond to algebraic integers all of whose conjugates (given by eigenvalues of the Frobenius endomorphism on the first cohomology group or Tate module) have absolute value √q. Tate showed that the map taking an isogeny class to the eigenvalues of the Frobenius is injective, and Taira Honda showed that this map is surjective, and therefore a bijection. (en)
  • Inom matematiken är Honda–Tates sats ett resultat som klassificerar abelska varieteter över ändliga kroppar upp till . Satsen säger att isogeniklasserna av enkla abelska varieteter över en ändlig kropp av ordning q korresponderar till algebraiska heltal vars alla konjugat (som ges av egenvärdena av av första kohomologigruppen eller ) har absolut värde √q. bevisade att avbildningen som tar isogeniklassen till egenvärdena av Frobeniusendomorfin är injektiv, och bevisade att den är surjektiv, och härmed en bijektion. (sv)
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