On finite generation of Noetherian algebras over two-dimensional regular local rings

2020/04/19 by Dutta, Amartya Kumar, Gupta, Neena, Onoda, Nobuharu
#13H05 #13J10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13E15 #Secondary: 13F20

paper · doi:10.48550/arxiv.2004.08869

Abstract

Let R be a complete regular local ring with an algebraically closed residue field and let A be a Noetherian R-subalgebra of the polynomial ring R[X]. It has been shown in \citeDO2 that if dim R=1, then A is necessarily finitely generated over R. In this paper, we give necessary and sufficient conditions for A to be finitely generated over R when dim R=2 and present an example of a Noetherian normal non-finitely generated R-subalgebra of R[X] over R= \mathbb C[[u, v]].

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