Discrete adelic groups

We show how to define discrete adelic groups which are related to infinitely generated discrete Heisenberg groups. This can be done not only for schemes of dimension $2$, but quite surprisingly for schemes of dimension $1$ and even of dimension $0$. Connections with $K$-theory, direct image problem and representation theory will be explained. It's useful, but not obligatory to look into my talk “A new kind of functoriality in the Langlands theory” or its slides from the attached file.