Cirici, JoanaGuillén Santos, Francisco2015-02-032015-02-032014-11-051472-2747https://hdl.handle.net/2445/62303Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ 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. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.31 p.application/pdfeng(c) Mathematical Sciences Publishers (MSP), 2014Singularitats (Matemàtica)Teoria de l'homotopiaSingularities (Mathematics)Homotopy theoryinfo:eu-repo/semantics/article6462692015-02-03info:eu-repo/semantics/openAccess