Abstract

Classically, since $\mathbb{Z}/p$ is a field, any module over the Eilenberg—MacLane spectrum $H\mathbb{Z}/p$ splits as a wedge of suspensions of $H\mathbb{Z}/p$ itself.  Equivariantly, cohomology and the module theory of $G$-equivariant Eilenberg—MacLane spectra are much more complicated. For the cyclic group $G=C_p$ and the constant Mackey functor $\underline{\mathbb{Z}}/p$, there are infinitely many indecomposable $H\underline{\mathbb{Z}}/p$-modules.  Previous work together with Dugger and Hazel classified all indecomposable $H\underline{\mathbb{Z}}/2$-modules for the group $G=C_2$.  The isomorphism classes of indecomposables fit into just three families.  By contrast, we show for $G=C_p$ with $p$ an odd prime, the classification of indecomposable $H\underline{\mathbb{Z}}/p$-modules is wild.  This is joint work in progress with Grevstad.