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In mathematics, Tate's isogeny theorem, proved by Tate (1966), states that two abelian varieties over a finite field are isogeneous if and only if their Tate modules are isomorphic (as Galois representations).

References

Mumford, David (2008) [1970], Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Providence, R.I.: American Mathematical Society, ISBN 9788185931869, MR 0282985, OCLC 138290
Tate, John (1966), "Endomorphisms of abelian varieties over finite fields", Inventiones Mathematicae 2: 134–144, doi:10.1007/BF01404549, ISSN 0020-9910, MR 0206004

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