Homological algebra with locally compact abelian groups

By N. Hoffmann, Markus Spitzweck. 2005

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In this article we study locally compact abelian groups using the language of derived categories. We define a derived Hom-functor on the bounded derived category of LCA groups with values in the derived category of Hausdorff topological abelian groups. We introduce a smallness condition for LCA groups and show that the category of such groups has a natural tensor product and internal Hom. Derived versions of these yield closed tensor triangulated categories which may be of arithmetical interest.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/911c36e0189fc2c2942626472e5db47d3a526484