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 will study profinite/pro-p analogs of Selmer varieties to better understand non-abelian first cohomology sets. We will adapt the results of Lawrence–Venkatesh for p-adic period maps to the case of Selmer sections, aiming at finiteness results for the local components that can occur in Selmer sections. We will also 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