English

Polarizations and Grothendieck's Standard Conjectures

Algebraic Geometry 2007-05-23 v3 Number Theory

Abstract

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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Cite

@article{arxiv.math/0103175,
  title  = {Polarizations and Grothendieck's Standard Conjectures},
  author = {J. S. Milne},
  journal= {arXiv preprint arXiv:math/0103175},
  year   = {2007}
}

Comments

12 pages published version

R2 v1 2026-07-22T16:37:51.924Z