Equivariant Eilenberg-Mac Lane spectra in cyclic $p$-groups

Abstract

In this paper we compute $RO(G)$-graded homotopy Mackey functors of $H\underline{\mathbb{Z}}$, the Eilenberg-Mac Lane spectrum of the constant Mackey functor of integers for cyclic p-groups and give a complete computation for $G=C_{p^2}$ . We also discuss homological algebra of $\underline{\mathbb{Z}}$-modules for cyclic $p$-groups, and interactions between these two. The goal of this paper is to understand various slice spectral sequences as $RO(G)$-graded spectral sequences of Mackey functors.

arXiv comment52 pages. Title is updated and major parts of the paper is rewritten. Comments welcome

References in corpus (1)

• G-symmetric monoidal categories of modules over equivariant commutative ring spectra

Cited by in corpus (6)

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• The $RO(C_4)$ cohomology of the infinite real projective space
• $C_2$ equivariant characteristic classes over the rational Burnside ring
• Bredon Cohomology of Polyhedral Products