Polarizations and Grothendieck's Standard Conjectures
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math.NT
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abelianconjecturehodgestandardvarietiesgrothendieckholdsprove
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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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