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Lambda Module structure on higher $K$-groups

Sourayan Banerjee, Vivek Sadhu

Abstract

In this article, we show that for a quasicompact scheme $X$ and $n>0,$ the $n$-th $K$-group $K_{n}(X)$ is a $λ$-module over a $λ$-ring $K_{0}(X)$ in the sense of Hesselholt.

Lambda Module structure on higher $K$-groups

Abstract

In this article, we show that for a quasicompact scheme and the -th -group is a -module over a -ring in the sense of Hesselholt.
Paper Structure (8 sections, 11 theorems, 22 equations)

This paper contains 8 sections, 11 theorems, 22 equations.

Table of Contents

  1. introduction
  2. Preliminaries
  3. Symmetric functions
  4. The polynomials $P_{n, m}$ and $P_{n}$
  5. $\lambda$-rings
  6. Adams operations
  7. $\lambda$-ring structure on $K_{*}(X)$
  8. $\lambda$-module structure on higher $K$-groups

Key Result

Theorem 1.2

For any quasicompact scheme $X$ and $n>0,$ each $K_{n}(X)$ is a $\lambda$-module over $K_{0}(X).$

Theorems & Definitions (25)

  • Definition 1.1
  • Theorem 1.2
  • Example 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • ...and 15 more