Arithmetic Quotients of the Bruhat-Tits Building for Projective GeneralLinear Groups in Positive Characteristic

Satoshi Kondo, Middle East Technical University, Northern Cyprus Campus, Guzelyurt, Turkish Republic of Northern Cyprus, and University of Tokyo, Kashiwa, Japan.. Seidai Yasuda, Hokkaido University, Sapporu, Japan.

Chapters 1. Introduction 2. Generalized simplicial complexes and their (co)homology 3. The Bruhat-Tits building and apartments 4. Arithmetic subgroups and modular symbols 5. Automorphic Forms with Steinberg at infinity 6. Double cosets for automorphic forms 7. Proof of Theorem 5.4.2 8. Universal Modular Symbols 9. On finite $p$-subgroups of arithmetic subgroups 10. Some spectral sequences 11. Proof for universal modular symbols 12. Comparison of modular symbols