Absence of torsion in orbit space

2020/07/15 by Sharma, Sampat
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.07545

Abstract

In this paper, we prove that if R is a local ring of dimension d, d≥ 2 and (1)/(d!)∈ R then the group \fracUm_d+1(R[X])E_d+1(R[X]) has no k-torsion, provided k∈ GL₁(R). We also prove that if R is a regular ring of dimension d, d≥ 2 and (1)/(d!)∈ R such that E_d+1(R) acts transitively on Um_d+1(R) then E_d+1(R[X]) acts transitively on Um_d+1(R[X]).

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