Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on $\mathbb{T}$-valued cohomology groups of algebraic group
  actions   We prove that for a weakly mixing algebraic action $\sigma:
G\curvearrowright(X,\nu)$, the $n$-cohomology group $H^n(G\curvearrowright X;
\mathbb{T})$, after quotienting out the natural subgroup $H^n(G,\mathbb{T})$,
contains $H^n(G,\widehat{X})$ as a natural subgroup for $n=1$. If we further
assume the diagonal actions $\sigma^2, \sigma^4$ are $\mathbb{T}$-cocycle
superrigid and $H^2(G, \widehat{X})$ is torsion free as an abelian group, then
the above also holds true for $n=2$. Applying it for principal algebraic
actions when $n=1$, we show that $H^2(G,\mathbb{Z}G)$ is torsion free as an
abelian group when $G$ has property (T) as a direct corollary of Sorin Popa's
cocycle superrigidity theorem; we also use it (when $n=2$) to answer,
negatively, a question of Sorin Popa on the 2nd cohomology group of Bernoulli
shift actions of property (T) groups.

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The categories of this paper are: eess
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: quant-ph