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On the formal cohomology of local rings | Peter Schenzel
; | Date: |
16 Apr 2007 | Subject: | Commutative Algebra (math.AC); Algebraic Geometry (math.AG) | Abstract: | Let $mathfrak a$ denote an ideal of a local ring $(R, mathfrak m).$ Let $M$
be a finitely generated $R$-module. There is a systematic study of the formal
cohomology modules $varprojlim HH^i(M/mathfrak a^nM), i in mathbb Z.$ We
analyze their $R$-module structure, the upper and lower vanishing and
non-vanishing in terms of intrinsic data of $M,$ and its functorial behavior.
These cohomology modules occur in relation to the formal completion of the
punctured spectrum $Spec R setminus V(mathfrak m).$ As a new cohomological
data there is a description on the formal grade $fgrade(mathfrak a, M)$
defined as the minimal non-vanishing of the formal cohomology modules. There
are various exact sequences concerning the formal cohomology modules. Among
them a Mayer-Vietoris sequence for two ideals. It applies to new connectedness
results. There are also relations to local cohomological dimensions. | Source: | arXiv, arxiv.0704.2005 | Services: | Forum | Review | PDF | Favorites |
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