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Tate’s Conjecture on the Endomorphisms of Abelian Varieties

Norbert Schappacher

Open publisher page 3 citations

Abstract

Following Faltings and using older arguments due to Tate and Zarhin, we shall deduce, from the diophantine result [F2],II 4.3, Tate’s conjectural description of the endomorphisms of abelian varieties over number fields, in terms of ℓ-adic representations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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What this paper is about

Following Faltings and using older arguments due to Tate and Zarhin, we shall deduce, from the diophantine result [F2],II 4.3, Tate’s conjectural description of the endomorphisms of abelian varieties over number fields, in terms of ℓ-adic representations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Available abstract

Following Faltings and using older arguments due to Tate and Zarhin, we shall deduce, from the diophantine result [F2],II 4.3, Tate’s conjectural description of the endomorphisms of abelian varieties over number fields, in terms of ℓ-adic representations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Key concepts: Endomorphism, Abelian group, Mathematics, Conjecture, Arithmetic of abelian varieties, Diophantine equation, Pure mathematics, Algebra over a field

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