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2018•arXiv (Cornell University)Open access

Tate Conjecture And Finiteness of Abelian Varieties over Finite Field

Anningzhe Gao

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Abstract

In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.

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What this paper is about

In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.

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Available abstract

In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.

Key concepts: Conjecture, Abelian group, Mathematics, Finite field, Field (mathematics), Pure mathematics, Arithmetic of abelian varieties, Combinatorics

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