Exterior power operations on relative K-theory

2026/07/10 by Bernhard Köck, Jane Turner · 2 voices
Mathematics · #math.KT #math.AG

paper · pdf

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.

Citations

• Comparison of Exterior Power Operations on Higher K-Theory of Schemes
• Exterior power operations on higher K-groups via binary complexes
• Non-additive functors and Euler characteristics
• Relative algebraic K-theory by elementary means
• Symmetric powers of Galois modules on Dedekind schemes
• Computing the homology of Koszul complexes
• Higher Algebraic K-Theory of Schemes and of Derived Categories

Discussions

• Bernhard K\"ock, Jane Turner Exterior power operations on relative K-theory https://arxiv.org/abs/2607.09538 [bsky, 0 points, 0 comments]
• Bernhard K\"ock, Jane Turner: Exterior power operations on relative K-theory https://arxiv.org/abs/2607.09538 https://arxiv.org/pdf/2607.09538 https://arxiv.org/html/2607.09538 [bsky, 0 points, 0 comments]

Related

• Comparison of Exterior Power Operations on Higher K-Theory of Schemes
• Exterior power operations on higher K-groups via binary complexes
• Two Formulae for Exterior power operations on higher K-groups
• Combinatorial relative algebraic K-theory
• Relative algebraic K-theory by elementary means