Invariant rings of modular P-groups

We consider a finite group acting as linear substitutions on a polynomial ring and study the corresponding ring of invariants. Computing the invariant ring and finding its ring theoretical properties is a classical problem. We focus on the modular case where the characteristic of the field divides the order of the group. We review invariants of basic modular actions and give explicit descriptions of invariants of small dimensional actions. We also discuss a recent algorithm that computes the invariant ring of a modular p-group up to a localization and we apply this algorithm to invariants of indecomposable representations of a cyclic group of prime order.