BaumSchneider cohomology

General Introduction
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Connections to Number Theory
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History and Applications
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Some Research Articles
Baum and Schneider article abstract: For the action of a locally compact and totally disconnected group G (the most important examples of such being all discrete groups as well as all padic reductive groups) on a pair of locally compact spaces X and Y we construct, by sheaf theoretic means, a new equivariant and bivariant cohomology theory. In contrast to the classical Borel construction of equivariant cohomology our construction is not localized in the unit element of the group. If we take for the first space Y "the" universal proper Gaction then we obtain for the second space its delocalized equivariant homology. All this is in exact formal analogy to the definition of equivariant Khomology by Baum, Connes, Higson starting from the bivariant equivariant Kasparov KKtheory. Under certain basic finiteness conditions on the first space Y we conjecture the existence of a Chern character from the equivariant Kasparov KKtheory of Y and X into our cohomology theory made twoperiodic which becomes an isomorphism upon tensoring the KKtheory with the complex numbers. This conjecture is proved in this paper for profinite groups G. An essential role in our construction is played by a bivariant version of Segal localization which we establish for KKtheory.
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