Exterior power operations on relative K-theory

Bernhard Köck; Jane Turner

Exterior power operations on relative K-theory

K-Theory and Homology 2026-07-10 v1 Algebraic Geometry

Authors: Bernhard Köck , Jane Turner

Abstract

We algebraically construct exterior power operations on higher relative algebraic K-groups and prove their desired properties such as the expected behaviour with respect to (tensor) products and composition. This builds on Grayson's description of relative K-groups in terms of explicit generators and relations and on work by Harris, the first author and Taelman for (absolute) K-groups. Among the new features in our approach is the observation that the product axiom in the classical notion of a lambda-ring is redundant.

Keywords

relative K-theory exterior power operations lambda-ring algebraic K-groups Grayson description

Cite

@article{arxiv.2607.09538,
  title  = {Exterior power operations on relative K-theory},
  author = {Bernhard Köck and Jane Turner},
  journal= {arXiv preprint arXiv:2607.09538},
  year   = {2026}
}

Comments

26 pages