  We leverage the results of the prequel in combination with a theorem of D.
Orlov to yield some results in Hodge theory of derived categories of
factorizations and derived categories of coherent sheaves on varieties. In
particular, we provide a conjectural geometric framework to further understand
M. Kontsevich's Homological Mirror Symmetry conjecture. We obtain new cases of
a conjecture of Orlov concerning the Rouquier dimension of the bounded derived
category of coherent sheaves on a smooth variety. Further, we introduce actions
of $A$-graded commutative rings on triangulated categories and their associated
Noether-Lefschetz spectra as a new invariant of triangulated categories. They
are intended to encode information about algebraic classes in the cohomology of
an algebraic variety. We provide some examples to motivate the connection.
