Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the formal cohomology of local rings   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.

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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg