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.

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.