Galois representations in anabelian geometry (B02)

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

This project studies Galois sections for hyperbolic curves over number fields with p-adic methods. We so far adapted the p-adic period map of Lawrence–Venkatesh to the case of Selmer sections, and we will continue to use this tool aiming for uniformity of bounds for the local components that can occur in Selmer sections. Arboreal Galois representations will be studied as combinatorial analogues of the linear Galois representations attached to Galois sections arising form local systems on the curve. In a third part of the project, we will further develop the modularity method for Galois sections and apply it to the Fermat curve.

• 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. Jakob Stix