p-adic non-abelian Hodge theory (C06)

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

This project studies p-adic analogues of the Simpson correspondence using v-vector bundles, a new class of vector bundles on p-adic varieties. Our first goal is to use moduli spaces of v-vector bundles to make progress on an open question of Faltings about the p-adic Simpson correspondence for curves. Second, we aim for a moduli-theoretic description of v-vector bundles in arithmetic situations towards applications to the p-adic Local Langlands programme. Third, we apply v-vector bundles to study new analogues of non-Kähler manifolds in p-adic geometry.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 326: Geometry and Arithmetic of Uniformized Structures (GAUS)
• Applicant Institution: Goethe-Universität Frankfurt am Main
• Project Heads: Dr. Ben Heuer; Professorin Dr. Annette Werner