This is a mini workshop on plectic program and its p-adic variant at RUC.

Date: April 17, 2025

Place: Room 4107，School of Mathematics, Renmin University of China

Title: Plectic weight filtration on cohomology of Hilbert modular varieties

Speaker: Zhiyou Wu (MCM)

Time: 14:00-15:00

Abstract: The plectic program is proposed by Jan Nekovar and Tony Scholl to uncover some hidden symmetries of Hilbert modular varieties. It would yield exciting new results on special values of L functions once established. In this talk, I will report my work on the construction of plectic weight filtration, providing evidence of the plectic conjectures.

Title : Künneth theorem for the p-adic étale cohomology of Drinfeld’s symmetric space

Speaker: Arnaud Vanhaecke (MCM)

Time: 15:30-16:30

Abstract: In this work we prove a Künneth formula for the p-adic étale cohomology of Drinfeld’s symmetric space. The genesis of this project is to study the p-adic étale cohomology of the p-adic upper-half plane’s Weil restriction and how this cohomology realizes a plectic intermediate for the p-adic local Langlands correspondence in a particular case. Künneth’s theorem is in general false for the restriction of period spaces but we conjecture that there should still be a plectic structure. I will explain this p-adic plectic conjecture and its relations with the weight filtration on crystalline cohomology. This is joint work with N. Marquis.