A Calabi-Yau variety, in the algebraic convention used here, is a smooth variety that is a geometrically irreducible projective
variety with trivial canonical bundle (Brantner
2026). This convention does not impose vanishing of intermediate coherent cohomology.
A Calabi-Yau threefold is strict when 
.
Ordinary Calabi-Yau threefolds over finite fields, and strict 1-ordinary threefolds, satisfy the integral geometric Tate conjecture (Brantner 2026). Ordinarity means that the Hodge and Newton polygons agree. The convention differs in scope from definitions of Calabi-Yau spaces that include additional analytic or topological hypotheses.
