Exterior power operations on higher $K$-groups via binary complexes
K-Theory and Homology
2017-06-14 v3 Algebraic Geometry
Representation Theory
Abstract
We use Grayson's binary multicomplex presentation of algebraic -theory to give a new construction of exterior power operations on the higher -groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a -ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal -ring on one generator.
Cite
@article{arxiv.1607.01685,
title = {Exterior power operations on higher $K$-groups via binary complexes},
author = {Tom Harris and Bernhard Köck and Lenny Taelman},
journal= {arXiv preprint arXiv:1607.01685},
year = {2017}
}
Comments
35 pages; v2: reference to a correspondence between Deligne and Grothendieck added; v3: referee's comments incorporated, to appear in Annals of K-Theory