Two formulae for exterior power operations on higher K-groups

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Harris, Tom¹  Kock, Bernhard² 

[1] Univ Printing House,Shaftesbury Rd, Cambridge CB2 8BS, England

[2] Univ Southampton, Math Sci, Southampton SO17 1BJ, Hants, England

关键词: Exterior power operations;    Higher K-groups;    external products;    Cauchy decomposition;    Cross-effect;    Modified Milnor K-groups;   

DOI  :  10.1016/j.jpaa.2019.03.001

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free