Grothendieck's Hodge standard conjecture for abelian varieties
Claims the Hodge standard conjecture for l-adic etale cohomology for all abelian varieties in arbitrary characteristic, deduced from the paper's CM Hodge theorem via Milne 2002. It does not address the standard conjectures for other varieties, the Lefschetz standard conjecture beyond what the abelian case already gives, or crystalline cohomology.
Exact FrontierDelta
Scope and record
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: Grothendieck's Hodge standard conjecture for abelian varieties · Hodge standard conjecture for abelian varieties
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Lineage and corrections
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
VibeMathed record: Grothendieck's Hodge standard conjecture for abelian varieties evidence for this event
Claims the Hodge standard conjecture for l-adic etale cohomology for all abelian varieties in arbitrary characteristic, deduced from the paper's CM Hodge theorem via Milne 2002. It does not address the standard conjectures for other varieties, the Lefschetz standard conjecture beyond what the abelian case already gives, or crystalline cohomology. parent of this event
Grothendieck's Hodge standard conjecture for abelian varieties parent of this event
Earlier edition (September 30, 2026) evidence for this event
Act on this frontier