## Spanier–Whitehead duality in the $K(2)$-local category at $p=2$

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- by Irina Bobkova PDF
- Proc. Amer. Math. Soc.
**148**(2020), 5421-5436 Request permission

## Abstract:

The fixed point spectra of Morava $E$-theory $E_n$ under the action of finite subgroups of the Morava stabilizer group $\mathbb {G}_n$, and their $K(n)$-local Spanier–Whitehead duals can be used to approximate the $K(n)$-local sphere in certain cases. For any finite subgroup $F$ of $\mathbb {G}_2$ at $p=2$ we prove that the $K(2)$-local Spanier–Whitehead dual of the spectrum $E_2^{hF}$ is $\Sigma ^{44}E_2^{hF}$. These results are analogous to the known results at height 2 and $p=3$. The main computational tool we use is the topological duality resolution spectral sequence for the spectrum $E_2^{h\mathbb {S}_2^1}$ at $p=2$.## References

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## Additional Information

**Irina Bobkova**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 1124377
- ORCID: 0000-0001-8775-2691
- Email: ibobkova@math.tamu.edu
- Received by editor(s): June 24, 2018
- Received by editor(s) in revised form: December 24, 2018, July 2, 2019, and February 24, 2020
- Published electronically: September 4, 2020
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140, while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, CA, during the Spring 2019 semester, and Grant No. DMS-1638352 and DMS-2005627
- Communicated by: Mark Behrens
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5421-5436 - MSC (2010): Primary 55P25, 55P42, 55T25
- DOI: https://doi.org/10.1090/proc/15078
- MathSciNet review: 4163853