What is called Hodge-filtered cohomology [Hopkins & Quick (2014)] is the variant of differential generalized cohomology obtained by passing from real differential geometry to complex geometry: Where differential cohomology by default pairs a given Whitehead-generalized cohomology theory of underlying topological spaces with the degree-filtered -valued de Rham complexes of differential forms on real smooth manifolds, the Hodge-filtered variant pairs instead with the Hodge filtered -valued...