Structure theorems for the heart of LCA
Category Theory
2025-12-04 v1 Group Theory
K-Theory and Homology
Number Theory
Abstract
Cohomology theories with values in LCA (locally compact abelian) groups suffer from the problem that the latter do not form an abelian category. However, the category LCA has a canonical abelian category envelope, the heart of a suitable t-structure. It adds formal cokernel objects. We show the surprising result that these abstract cokernels can also be interpreted as Hausdorff topological abelian groups, at least up to lattice isogenies. These need not be locally compact.
Keywords
Cite
@article{arxiv.2512.03338,
title = {Structure theorems for the heart of LCA},
author = {Oliver Braunling and Fei Ren},
journal= {arXiv preprint arXiv:2512.03338},
year = {2025}
}
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49 pages