Cusp forms on Drinfeld period domains (A07)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124

Building on recent developments, we shall investigate arithmetic-geometric and combi-natorial aspects of cusp forms on certain moduli varieties, uniformized by Drinfeld period domains mostly over function fields and beyond the well-established case of rank 2. To Drinfeld cusp forms of rank at least 3 we shall attach motives, also in the sense of Mornev shtukas, prove an Eichler–Shimura isomorphism, explore motivic weights and work toward a geometric Jacquet–Langlands type correspondence. The link to harmonic co¬chains and boundary distributions, also for rank at least 3, shall be further developed. Possible applications are to Hecke-stable filtrations and to higher rank L-invariants.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 326: Geometry and Arithmetic of Uniformized Structures (GAUS)
• Applicant Institution: Goethe-Universität Frankfurt am Main
• Project Head: Professor Dr. Gebhard Böckle