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Degree bounds for modular covariants (2001.08052v1)

Published 22 Jan 2020 in math.AC and math.RT

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 $V \rightarrow W$, 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 $d$.

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