Some results on local cohomology of polynomial and formal power series rings: the one dimensional case

TL;DR

This paper investigates the finiteness properties of local cohomology in polynomial and formal power series rings, providing partial answers to existing questions in the one-dimensional case.

Contribution

It offers new results on local cohomology finiteness for polynomial and power series rings, addressing a specific open question.

Findings

Established finiteness results for local cohomology in one-dimensional cases

Provided partial affirmative answers to a question by Nz-Betancourt

Enhanced understanding of local cohomology behavior in polynomial and power series rings

Abstract

In this paper, we prove several results on the finiteness of local cohomology of polynomial and formal power series rings. In particular, we give a partial affirmative answer for a question of L. N\'{u}\~{n}ez-Betancourt in [J. Algebra 399 (2014), 770--781].