Cohomology of arithmetic groups and periods of automorphic forms
This is a an impressively successful expository article. Based upon his 2014 Takagi Lectures, this is an example-rich introduction to the cohomology of arithmetic groups and in particular a motivation for the author's project to ``explain'' the ``copies of the cohomology of a torus'' that appear in the tempered cohomology of these groups. The conjectured explanation is that there is a ``hidden action of certain motivic cohomology groups'' at hand. (A formal statement of this main conjecture is given.) The conjecture rests ``on a large web of other conjectures'' but this is perhaps the exciting aspect, as this conjecture ``produces testable predictions'', which the author with co-workers has verified in some cases. But, this article is not aimed at the leading experts in this highly technical area, but rather at a fairly general audience, and thus the emphasis on as elementary examples as possible, while the various footnotes and comments indicate how one one fills in the arguments and where to find precise definitions.
scientific article; zbMATH DE number 6704093
scientific article