| 释义 |
- References
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 {{radic|q}}. {{harvs|txt|last=Tate|authorlink=John Tate|year=1966}} showed that the map taking an isogeny class to the eigenvalues of the Frobenius is injective, and {{harvs|txt|authorlink= Taira Honda|first=Taira|last=Honda|year=1968}} showed that this map is surjective, and therefore a bijection.References- {{Citation | last1=Honda | first1=Taira | title=Isogeny classes of abelian varieties over finite fields | url=http://projecteuclid.org/euclid.jmsj/1260463295 | doi=10.2969/jmsj/02010083 | mr=0229642 | year=1968 | journal=Journal of the Mathematical Society of Japan | issn=0025-5645 | volume=20 | pages=83–95}}
- {{Citation | last1=Tate | first1=John | author1-link=John Tate | title=Endomorphisms of abelian varieties over finite fields | doi=10.1007/BF01404549 | mr=0206004 | year=1966 | journal=Inventiones Mathematicae | issn=0020-9910 | volume=2 | pages=134–144}}
- {{Citation | last1=Tate | first1=John | author1-link=John Tate | title=Séminaire Bourbaki vol. 1968/69 Exposés 347-363 | publisher=Springer Berlin / Heidelberg | series=Lecture Notes in Mathematics | doi=10.1007/BFb0058807 | year=1971 | volume=179 | chapter=Classes d'isogénie des variétés abéliennes sur un corps fini (d'après T. Honda) | chapterurl=http://www.numdam.org/item?id=SB_1968-1969__11__95_0 | pages=95–110}}
{{DEFAULTSORT:Honda-Tate theorem}}{{abstract-algebra-stub}} 1 : Theorems in algebraic geometry |