Definition 45.7.3. Let $k$ be an algebraically closed field. Let $F$ be a field of characteristic $0$. A *classical Weil cohomology theory* over $k$ with coefficients in $F$ is given by data (D1), (D2), and (D3) satisfying Poincaré duality, the Künneth formula, and compatibility with cycle classes, more precisely, satisfying (A), (B), and (C).

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