Étale cohomology of rigid analytic spaces.
de Jong, Johan, van der Put, Maurius (1996)
Documenta Mathematica
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de Jong, Johan, van der Put, Maurius (1996)
Documenta Mathematica
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2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15. We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new...
Andrzej Czarnecki (2014)
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A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.
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A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.