Associated primes of local cohomology of flat extensions with regular fibers and Sigma-finite D-modules

作者：Nunez Betancourt Luis^*

来源：Journal of Algebra, 2014, 399: 770-781.

DOI：10.1016/j.jalgebra.2013.10.010

• Local cohomology
• Associated primes
• D-modules

In this manuscript, we study the following question raised by Mel Hochster: Let (R, m, K) be a local ring and S be a flat extension with regular closed fiber. Is V(mS) boolean AND Ass(s) H-l(i)(S) finite for every ideal I subset of S and i is an element of N? We prove that the answer is positive when S is either a polynomial or a power series ring over R and dim(R/I boolean AND R) <= 1. In addition, we analyze when this question can be reduced to the case where S is a power series ring over R. An important tool for our proof is the use of Sigma-finite D-modules, which are not necessarily finitely generated as D-modules, but whose associated primes are finite. We give examples of this class of D-modules and applications to local cohomology.

• 出版日期2014-2-1