Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 57, Number 1 (2013), 279-294.
Local cohomology modules of polynomial or power series rings over rings of small dimension
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.
Illinois J. Math., Volume 57, Number 1 (2013), 279-294.
First available in Project Euclid: 23 June 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D45: Local cohomology [See also 14B15]
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