  Let X be a smooth complex algebraic variety. Morgan [Mor78] showed that the
rational homotopy type of X is a formal consequence of the differential graded
algebra defined by the first term of its weight spectral sequence. In the
present work we generalize this result to arbitrary nilpotent complex algebraic
varieties (possibly singular and/or non-compact) and to algebraic morphisms
between them. The result for algebraic morphisms generalizes the Formality
Theorem of [DGMS75] for compact K\"ahler varieties, filling a gap in Morgan's
theory concerning functoriality over the rational numbers. As an application,
we study the Hopf invariant of certain algebraic morphisms using intersection
theory.
