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SOME NUMERICAL INVARIANTS OF LOCAL RINGS JOSEP `ALVAREZ MONTANER
 

Summary: SOME NUMERICAL INVARIANTS OF LOCAL RINGS
JOSEP `ALVAREZ MONTANER
Abstract. Let R be a formal power series ring over a field of characteristic
zero and I R be any ideal. The aim of this work is to introduce some
numerical invariants of the local rings R/I by using the theory of algebraic
D-modules. More precisely, we will prove that the multiplicities of the char-
acteristic cycle of the local cohomology modules Hn-i
I (R) and Hp
p(Hn-i
I (R)),
where p R is any prime ideal that contains I, are invariants of R/I.
1. Introduction
Let (R, m, k) be a regular local ring of dimension n containing the field k, and
A a local ring which admits a surjective ring homomorphism : R-A. Set
I = Ker . G. Lyubeznik [10] defines a new set of numerical invariants of A by
means of the Bass numbers p,i(A) := µp(m, Hn-i
I (R)) := dimkExtp
R(k, Hn-i
I (R)).
This invariant depends only on A, i and p, but neither on R nor on . Completion

  

Source: Alvarez Montaner, Josep - Departament de Matemątica Aplicada I, Universitat Politčcnica de Catalunya

 

Collections: Mathematics