Abstract:
There are multiple interesting ways to promote an ordinary commutative ring to an equivariant ring spectrum. We will relate the module categories of such and then focus on modules over the Eilenberg-MacLane spectrum associated to a constant Green functor. Here we can define modular fixed point functors which are linear analogues of geometric fixed points. We then explain how these recover the modular fixed points on derived permutation modules introduced by Balmer-Gallauer and how they help to tackle the Picard group of modules over a constant Green functor.