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 $V\to W$, and is a module over $k[V{]}^G$. We give a formula for the Noether bound $\beta (k[V,W{]}^G,k[V{]}^G)$, i.e. the minimal degree $d$ such that $k[V,W{]}^G$ is generated over $k[V{]}^G$ by elements of degree at most $d$.

6 pages