SPANIER-WHITEHEAD DUALITY IN THE K(2)-LOCAL CATEGORY AT p=2 uri icon

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 the height 2 Morava stabilizer group 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 $E_2^{hmathbb{S}_2^1}$ at p=2.

published proceedings

  • PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

altmetric score

  • 1

author list (cited authors)

  • Bobkova, I.

citation count

  • 1

complete list of authors

  • Bobkova, Irina

publication date

  • September 2020