Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: De-Rham theorem and Shapiro lemma for Schwartz functions on Nash
  manifolds   In this paper we continue our work on Schwartz functions and generalized
Schwartz functions on Nash (i.e. smooth semi-algebraic) manifolds. Our first
goal is to prove analogs of de-Rham theorem for de-Rham complexes with
coefficients in Schwartz functions and generalized Schwartz functions. Using
that we compute cohomologies of the Lie algebra of an algebraic group G with
coefficients in the space of generalized Schwartz sections of G-equivariant
bundle over a G-transitive variety M. We do it under some assumptions on
topological properties of G and M. This computation for the classical case is
known as Shapiro lemma.

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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex