Degree bounds for modular covariants

2020/01/22 by Elmer, Jonathan, Sezer, Müfit
#13A50 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2001.08052

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.

Related

• Modular Covariants of Cyclic Groups of Order p
• Cohen-Macaulay modules of covariants for cyclic p-groups
• On Some Applications of Group Representation Theory to Algebraic Problems Related to the Congruence Principle for Equivariant Maps
• Counterexamples to Norm Conjectures of Wehlau in Modular Invariant Theory
• Coinvariants for modular representations of cyclic groups of prime order