(see also Chern-Weil theory, parameterized homotopy theory)
group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The canonical line bundle on the product of an abelian group (abelian variety) and its dual Picard scheme. Alternatively its sheaf of sections: the Poincaré sheaf.
The idea is briefly summarized in
Lecture notes include
Textbook accounts include
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