Document Zbl 1055.14008

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Milne, J. S.

Polarizations and Grothendieck’s standard conjectures. (English) Zbl 1055.14008

Ann. Math. (2) 155, No. 2, 599-610 (2002).

Summary: 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.

Cited in 1 Document

MSC:

14C30	Transcendental methods, Hodge theory (algebro-geometric aspects)
14K15	Arithmetic ground fields for abelian varieties

Keywords:

quotient categories; motives over finite fields; abelian varieties; Hodge standard conjecture

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