Topological automorphic forms are a generalization of topological modular forms: where the latter come with the moduli space of elliptic curves, topological automorphic forms are associated to a given Shimura variety. Moreover, just as topological modular forms refine to the tmf-spectrum representing the corresponding cohomology theory, so every Shimura variety induces a cohomology theory .
|geometric object||multiplicative group||elliptic curve||Shimura variety|
The definition is due to
An introductory survey is in
Lecture notes include