2012/08/30 by Parker E. Lowrey, Parker Lowrey, Lowrey, Parker +2
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.KT #msc:14C40 #msc:19L10
paper · pdf · doi:10.48550/arxiv.1208.6325
34 pages
arxiv created 2012/08/30 · arxiv updated 2012/09/03
We define bivariant algebraic K-theory and bivariant derived Chow on the homotopy category of derived schemes over a smooth base. The orientation on the latter corresponds to virtual Gysin homomorphisms. We then provide a morphism between these two bivariant theories and compare the two orientations. This comparison then yields a homological and cohomological Grothendieck-Riemann-Roch formula for virtual classes.