Grothendieck-Riemann-Roch for derived schemes
Algebraic Geometry
2012-09-03 v1 Algebraic Topology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1208.6325,
title = {Grothendieck-Riemann-Roch for derived schemes},
author = {Parker Lowrey and Timo Schürg},
journal= {arXiv preprint arXiv:1208.6325},
year = {2012}
}
Comments
34 pages