The de-Rham theorem and Shapiro lemma for Schwartz functions on Nash manifolds |
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Authors: | Avraham Aizenbud Dmitry Gourevitch |
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Affiliation: | 1.Faculty of Mathematics and Computer Science,The Weizmann Institute of Science,Rehovot,Israel |
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Abstract: | 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 the de-Rham theorem for de-Rham complexes with coefficients in Schwartz functions and generalized Schwartz functions. Using that we compute the cohomologies of the Lie algebra g 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 the Shapiro lemma. |
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