Two formulae for exterior power operations on higher K-groups

Abstract

Exterior power operations on the higher K-groups of a quasi-compact scheme have recently been constructed by Taelman and the authors by purely algebraic means. In this paper, we prove two formulae that help to compute these operations. The first is a formula for exterior powers of external products. The second is a formula for exterior powers of n-cubes, i.e., of acyclic binary multi-complexes supported on [0, 1] n . These formulae provide evidence for the expectation that our exterior power operations agree with those defined by Hiller.

Comparison of Exterior Power Operations on Higher K-Theory of Schemes

“…We now mention some further papers about operations on higher K-theory. In [HK19], Harris and the first author have provided some early evidence that the operations defined in [HKT17] agree with those defined by Hiller in [Hil81] for affine schemes. Grayson has already shown in [Gra89] that his operations agree with Hiller's and those defined by Kratzer in [Kra80].…”