Polarizations and Grothendieck's Standard Conjectures

Mathematics – Algebraic Geometry

Scientific paper

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12 pages published version

Scientific paper

We prove that Grothendieck's Hodge standard conjecture holds for abelian
varieties in arbitrary characteristic if the Hodge conjecture holds for complex
abelian varieties of CM-type. For abelian varieties with no exotic algebraic
classes, we prove the Hodge standard conjecture unconditionally.

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