Grothendieck-Riemann-Roch for derived schemes

Abstract

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.

arXiv comment34 pages

References in corpus (1)

• The moduli stack and motivic Hall algebra for the bounded derived category

Cited by in corpus (2)

• K-theory and G-theory of derived algebraic stacks
• Derived Algebraic Geometry