Tate's isogeny theorem

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, vol. 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 (2): 134–144, Bibcode:1966InMat...2..134T, doi:10.1007/BF01404549, ISSN 0020-9910, MR 0206004, S2CID 245902