2015/12/17 by Rajsekhar Bhattacharyya, Bhattacharyya, Rajsekhar
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1512.05686
openalex publication_date 2015/12/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
For a Noetherian regular ring S and for a fixed ideal J⊂ S, assume that the associated primes of local cohomology module HiJ(S) does not contain p for some i≥ 0, and we call this as a property Pi,pJ,S or P for brevity. Recently, in Theorem 1.2 of \citeNu1, it is proved that in a Noetherian regular local ring S and for a fixed ideal J⊂ S, associated primes of local cohomology module HiJ(S) for i≥ 0 is finite, if it does not contain p. In this paper, we study how the property P (as mentioned above) can come down from unramified regular ring to ramified regular local ring. In \citeSW, Bockstein homomorphism is studied in the context to the finiteness of associated primes of local cohomology modules for the ring of integers. There it is shown that if p is nonzero divisor of Koszul homology then Bockstein homomorphism is a zero map (see, Theorem 3.1 of \citeSW). Here, in this paper, as a consequence of property P, we extend the result of Theorem 3.1 of \citeSW to the ramified regular local ring.