Topological automorphic forms

http://jp.arxiv.org/abs/math.AT/0702719

The idea of associating cohomology theories to Shimura varieties also does not originate with the authors ― Goerss, Lurie, and Morava have considered such matters. The authors are especially grateful to Jacob Lurie, who generously shared his work and results with the authors. (p.16)

Drinfeld modular variety や 非可換トーラスのモジュライに対するコホモロジーは？