ホッジ構造
The Hodge conjecture, may be neatly reformulated using motives: it holds iff the "Hodge realization" mapping any pure motive with rational coefficients (over a subfield formula_96 of formula_88) to its Hodge structure is a full functor formula_98 (rational Hodge structures). Here pure motive means pure motive with respect to homological equivalence.