nLab Witt-Burnside functor

Idea

Dress and Siebeneicher (DS88) generalized the Witt vector construction to the case of pro-$p$ groups for prime integer $p$. These functors, $W_G$, were originally defined for all profinite groups, $G$, and are now called Witt-Burnside functors due to the fact that they generalize both the $p$-typical (recovered when $G = \mathbb{Z}_p$ as an additive group) and ‘big’ Witt vector construction (recovered when $G = \hat{\mathbb{Z}}$), as well as Burnside functors (recovered as $W_G(\mathbb{Z})$).

Witt-Burnside functors have been used to study equivariant ring spectra as they arise as a left adjoint for Tambara functors.

References

• A. Dress, C. Siebeneicher, The Burnside ring of profinite groups and the Witt vector construction, Adv. Math., 70, (1988), 87–132.
• Lance Edward Miller, On the structure of Witt-Burnside rings attached to pro-p groups, (arXiv:1103.4644)