# nLab Anderson duality

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

duality

# Contents

## Idea

The stable (infinity,1)-category of spectra has a dualizing object (dualizing module) on a suitable subcategory of finite spectra. It is called the Anderson spectrum $I_{\mathbb{Z}}$ (Lurie, Example 4.3.9). The duality that this induces is called Anderson duality.

## Examples

The Anderson dual of the sphere spectrum is discussed in

The Anderson dual of KU is (complex conjugation-equivariantly) the 4-fold suspension spectrum $\Sigma^4 KU$ (Heard-Stojanoska 14, theorem 8.2).

Similarly tmf$[1/2]$ is Anderson dual to its 21-fold suspension (Stojanoska 12).

## References

### General

Original articles include

• D. W. Anderson, Universal coefficient theorems for K-theory, mimeographed notes, Univ. California, Berkeley, Calif., 1969.

• Zen-ichi Yosimura, Universal coefficient sequences for cohomology theories of CW-spectra, Osaka J. Math. 12 (1975), no. 2, 305–323. MR 52 #9212