p-adic Langlands correspondence and p-adic geometry of Shimura varieties

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610003
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: Imai Naoki 東京大学, 大学院数理科学研究科, 准教授 (90597775)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 志村多様体

Outline of Final Research Achievements

We studied p-adic geometry of Shimura varieties. In particular, we construct potentially good reduction locus, where motives don't degenerate, as an open subspace of the adic space associated to a Shimura variety over p-adic field. Further, we studied it's cohomology.
We studied also on the Kramer-Tunnel conjecture, which describe the epsilon factor of an elliptic curve over an local field by rational points of the elliptic curve. The conjecture was open in the characteristic two case. We showed the conjecture by reducing it to the characteristic zero case.

Free Research Field

数論