A Counterexample to Weitzenböck's Theorem in Characteristic p

2014/06/16 by Maguire, Stephen Joseph
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1406.4113

Abstract

In this paper we give a counterexample to Weitzenböck's Theorem in positive characteristic. Namely we show that if k is an algebraically closed field of characteristic p , there is an action of \mathbbG_a on \mathbbA⁵_k , induced by a linear representation of \mathbbG_a , such that the ring of invariants k[x₁,…,x₅]^\mathbbG_a is not finitely generated.

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