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The p-local stable Adams conjecture: Erratum

Prasit Bhattacharya, Nitu Kitchloo

Abstract

This erratum remedies errors in the literature pertaining to the stable Adams conjecture. As part of the above corrections, we also identify and fix two errors in section 4 of our recent article on the subject. We thank E. Fridelander for flagging these oversights and for offering helpful suggestions. This erratum is self-contained and also includes an appendix proving a version of Friedlander's classification result for sectioned fibrations of Gamma-spaces, after making appropriate changes to the original statement as indicated in the appendix.

The p-local stable Adams conjecture: Erratum

Abstract

This erratum remedies errors in the literature pertaining to the stable Adams conjecture. As part of the above corrections, we also identify and fix two errors in section 4 of our recent article on the subject. We thank E. Fridelander for flagging these oversights and for offering helpful suggestions. This erratum is self-contained and also includes an appendix proving a version of Friedlander's classification result for sectioned fibrations of Gamma-spaces, after making appropriate changes to the original statement as indicated in the appendix.

Paper Structure

This paper contains 6 sections, 19 theorems, 125 equations.

Table of Contents

  1. Discussion of errors and Introduction.
  2. Review of $\Gamma$-spaces after Bousfield, Friedlander and Segal.
  3. Graded topological permutative categories and $\Gamma$-spaces with rigid sections.
  4. From graded algebraic permutative categories to $\Gamma$-spaces with rigid sections.
  5. The fracture square and the $p$-local stable Adams conjecture.
  6. Friedlander's classification result for sectioned $X$-fibrations

Key Result

Theorem 1

(see Theorem PLAC) Fix $p,q$ to be any primes such that $p \neq q$. Recall the classical $p$-local $J$-homomorphism: where $\mathop{\mathrm{Pic}}\nolimits^{ev} {\bf S}_{(p)}$ is the even Picard space defined as $\Omega^{\infty} \mathop{\mathrm{pic}}\nolimits^{ev} {\bf S}_{(p)}$. Then $J$ lifts to a stable map such that $\underline{J}$ is invariant under precomposition with the Adams operation $\

Theorems & Definitions (92)

  • Theorem
  • Definition 2.1
  • Remark 1
  • Example 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Theorem 2.7
  • Definition 3.1
  • ...and 82 more