Author

Matt Broe

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Preprint Aug 2026

The Tate conjecture for abelian fourfolds over finite fields

We prove the Tate conjecture for abelian fourfolds over finite fields. This is the first resolution of the conjecture for all abelian varieties of a fixed dimension over finite fields since the work of Tate in the 1960s. The proof relies on techniques from Ancona's proof of the standard conjecture of Hodge type for abe...

Matt Broe · 1 citation · ⚡1