Degree bounds for modular covariants

Abstract

Let V, W be representations of a cyclic group G of prime order p over a field k of characteristic p. The module of covariants k[V, W]G is the set of G-equivariant polynomial maps V → W, and is a module over k[V ]G. We give a formula for the Noether bound β(k[V, W]G, k[V ]G), i.e. the minimal degree d such that k[V, W]G is generated over k[V ]G by elements of degree at most d