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Register a new userOn the Coefficients of $(mathbb{Z}/p)^n$-Equivariant Ordinary Cohomology with Coefficients in $mathbb{Z}/p$
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This note contains a generalization to $p>2$ of the authors previous calculations of the coefficients of $(mathbb{Z}/2)^n$-equivariant ordinary cohomology with coefficients in the constant $mathbb{Z}/2$-Mackey functor. The algberaic results by S.Kriz allow us to calculate the coefficients of the geometric fixed point spectrum $Phi^{(mathbb{Z}/p)^n}Hmathbb{Z}/p$, and more generally, the $mathbb{Z}$-graded coefficients of the localization of $Hmathbb{Z}/p_{(mathbb{Z}/p)^n}$ by inverting any chosen set of embeddings $S^0rightarrow S^{alpha_i}$ where $alpha_i$ are non-trivial irreducible representations. We also calculate the $RO(G)^+$-graded coefficients of $Hmathbb{Z}/p_{(mathbb{Z}/p)^n}$, which means the cohomology of a point indexed by an actual (not virtual) representation. (This is the non-derived part, which has a nice algebraic description.)
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