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

2012/07/08 by Luis Núñez‐Betancourt, Luis Nunez-Betancourt, Nunez-Betancourt, Luis
Mathematics · #13D45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13D45

paper · pdf · doi:10.48550/arxiv.1207.1896

16 pages. Minor corrections from previous version. Accepted in Illinois Journal of Mathematics

openalex publication_date 2012/07/08 · arxiv created 2013/10/30 · arxiv updated 2013/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 π is an nonzero divisor, then the same properties hold for prime ideals that contain π. 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.

Related

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