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

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. Nú˜nez-Betancourt in [J. Algebra 399 (2014), 770–781]. ... The motivation of this paper is the following conjecture of G. Lyubeznik: If R is a regular ring, then each local cohomology module Hi ... Motivated by the above finiteness results, M. Hochster raised the following re- lated questions: ... Question 1.1. Let (R, m,k) be a local ring and S a flat extension of R with ...