Vector bundles and local systems on non-Archimedean analytic spaces

• Applicant: Professorin Dr. Annette Werner
• Subject Area: Mathematics
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446443754

• Final Report Year: 2024

Final Report Abstract

The aim of this project was a deeper understanding of questions connected to p-adic versions of the Narasimhan-Seshadri and the Simpson correspondence with the help of new tools from p-adic Hodge theory. The results obtained include a study of vector bundles with numerically flat reduction after proper pullback based on Scholze’s theory of diamonds as well as new insights in log p-divisible groups and relative Fontaine-Laffaille modules.

Publications

• Local Systems on Diamonds and p-Adic Vector Bundles. International Mathematics Research Notices, 2023(15), 12785-12850.
  Mann, Lucas & Werner, Annette
  
• Divided prismatic Frobenius crystals of small height and the category MF
  Würthen, Matti
  
• Log p-divisible groups associated with log 1-motives. Canadian Journal of Mathematics, 76(3), 946-983.
  Würthen, Matti & Zhao, Heer
  
• Log prismatic Dieudonn´ theory for log p- divisible groups over OK
  Würthen, Matti & Zhao, Heer