The Tate conjecture for abelian varieties over finite fields
Claims the full rational Tate conjecture, in every codimension, for every abelian variety over every finite field, together with equality of numerical and l-adic homological equivalence, as a corollary of the paper's Hodge conjecture for CM abelian varieties via Milne 1999. It does not treat varieties other than abelian varieties, finitely generated fields other than finite fields, or integral coefficients. The paper notes that Milne's implication does not lift each Tate class to a Hodge class on one CM lift. The companion on split abelian eightfolds linked here was withdrawn on 6 October 2026 for a sign error; the release names only the Kuga-Satake and K3-product papers as depending on it, and this result is not withdrawn.
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Occurred: Sep 10, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Tate conjecture for abelian varieties over finite fields · Tate conjecture for abelian varieties over F_q
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
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Unreleased internal OpenAI model
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The Tate conjecture for abelian varieties over finite fields evidence for this event
This event attributed to Unreleased internal OpenAI model
Milne, Lefschetz motives and the Tate conjecture (1999): Hodge for CM implies Tate over finite fields evidence for this event
The Tate conjecture for abelian varieties over finite fields parent of this event
Claims the full rational Tate conjecture, in every codimension, for every abelian variety over every finite field, together with equality of numerical and l-adic homological equivalence, as a corollary of the paper's Hodge conjecture for CM abelian varieties via Milne 1999. It does not treat varieties other than abelian varieties, finitely generated fields other than finite fields, or integral coefficients. The paper notes that Milne's implication does not lift each Tate class to a Hodge class on one CM lift. The companion on split abelian eightfolds linked here was withdrawn on 6 October 2026 for a sign error; the release names only the Kuga-Satake and K3-product papers as depending on it, and this result is not withdrawn. parent of this event
VibeMathed record: The Tate conjecture for abelian varieties over finite fields evidence for this event
Algebraicity of Weil classes on split abelian eightfolds (OpenAI, 2026-09-18) evidence for this event
Earlier edition (September 30, 2026) evidence for this event
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