English

Associated primes of Local cohomology modules over Regular rings

Commutative Algebra 2016-03-09 v1

Abstract

Let RR be an excellent regular ring of dimension dd containing a field KK of characteristic zero. Let II be an ideal in RR. We show that Ass HId1(R)Ass \ H^{d-1}_I(R) is a finite set. As an application we show that if II is an ideal of height gg with height Q=gheight \ Q = g for all minimal primes of II then for all but finitely many primes PIP \supseteq I with height Pg+2height \ P \geq g +2, the topological space Spec(RP/IRP)Spec^\circ(R_P/IR_P) is connected.

Keywords

Cite

@article{arxiv.1411.2734,
  title  = {Associated primes of Local cohomology modules over Regular rings},
  author = {Tony J. Puthenpurakal},
  journal= {arXiv preprint arXiv:1411.2734},
  year   = {2016}
}