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SOME NUMERICAL INVARIANTS OF LOCAL RINGS 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
D­modules. More precisely, we will prove that the multiplicities of the char­
acteristic cycle of the local cohomology modules H n-i
I (R) and H p
p (H n-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) := µ p (m, H n-i
I (R)) := dim k Ext p
R (k, H n-i
I (R)).

  

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

 

Collections: Mathematics