Illinois Journal of Mathematics

Local cohomology modules of polynomial or power series rings over rings of small dimension

Luis Núñez-Betancourt

Full-text: Open access

Abstract

Let $A$ be a ring and $R$ be a polynomial or a power series ring over $A$. When $A$ has dimension zero, we show that the Bass numbers and the associated primes of the local cohomology modules over $R$ are finite. Moreover, if $A$ has dimension one and $\pi$ is an nonzero divisor, then the same properties hold for prime ideals that contain $\pi$. These results do not require that $A$ contains a field. As a consequence, we give a different proof for the finiteness properties of local cohomology over unramified regular local rings. In addition, we extend previous results on the injective dimension of local cohomology modules over certain regular rings of mixed characteristic.

Article information

Source
Illinois J. Math., Volume 57, Number 1 (2013), 279-294.

Dates
First available in Project Euclid: 23 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1403534496

Digital Object Identifier
doi:10.1215/ijm/1403534496

Mathematical Reviews number (MathSciNet)
MR3224571

Zentralblatt MATH identifier
1328.13021

Subjects
Primary: 13D45: Local cohomology [See also 14B15]

Citation

Núñez-Betancourt, Luis. Local cohomology modules of polynomial or power series rings over rings of small dimension. Illinois J. Math. 57 (2013), no. 1, 279--294. doi:10.1215/ijm/1403534496. https://projecteuclid.org/euclid.ijm/1403534496


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