2012/12/17 by Joana Cirici, J. Cirici, Francisco Guillén +1
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic cycle #Algebraic number #Algebraic variety #Dimension of an algebraic variety #Function field of an algebraic variety #Homotopy #Homotopy and Cohomology in Algebraic Topology #Intersection theory #Morphism #Polynomial and algebraic computation #Spectral sequence #math.AG #math.AT #msc:32S35 #msc:55P62
paper · pdf · doi:10.2140/agt.2014.14.3049
published as Algebr. Geom. Topol. 14 (2014) 3049-3079
arxiv created 2012/12/17 · openalex publication_date 2014/11/05 · arxiv updated 2014/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let 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 Khler 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.