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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the higher delta invariants
of a Gorenstein local ring


Author: Yuji Yoshino
Journal: Proc. Amer. Math. Soc. 124 (1996), 2641-2647
MSC (1991): Primary 13C14, 13D02, 13H10, 16G50
MathSciNet review: 1327054
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Abstract: Let $(R , \mathfrak {m} )$ be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by $\delta _R ^n(M)$ for each module $M$ and for each integer $n$. We propose a conjecture asking if $\delta _R ^n (R/\mathfrak {m} ^{\ell }) = 0$ for any positive integers $n$ and $\ell $. We prove that this is true provided the associated graded ring of $R$ has depth not less than $\operatorname {dim} R -1$. Furthermore we show that there are only finitely many possibilities for a pair of positive integers $(n, \ell )$ for which $\delta _R ^n (R/ \mathfrak {m} ^{\ell }) >0$.


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Additional Information

Yuji Yoshino
Affiliation: Institute of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Yoshida-Nihonmatsu, Sakyo-ku, Kyoto 606-01, Japan
Email: yoshino@math.h.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03376-X
PII: S 0002-9939(96)03376-X
Keywords: Cohen-Macaulay modules, Gorenstein ring, Cohen-Macaulay approximations
Received by editor(s): January 20, 1995
Received by editor(s) in revised form: March 9, 1995
Dedicated: To the memory of Professor Maurice Auslander
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society