Number Theory Seminar

Seminar information archive ~07/21Next seminarFuture seminars 07/22~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly

2022/10/12

17:00-18:00   Hybrid
Abhinandan (University of Tokyo)
Syntomic complex with coefficients (English)
[ Abstract ]
In the proof of $p$-adic crystalline comparison theorem, one of the most important steps in the approach of Fontaine and Messing is to establish a comparison between syntomic cohomology and p-adic étale cohomology via (Fontaine-Messing) period map. This approach was successfully generalized to the semistable case by Kato and a complete proof of crystalline and semistable comparison theorems for schemes was given by Tsuji. Few years ago, Colmez and Nizioł gave a new interpretation of the (local) Fontaine-Messing period map in terms of complexes of $(\varphi,\Gamma)$-modules and used it to prove semistable comparison theorem for $p$-adic formal schemes. We will present a generalisation (of crystalline version of this interpretation by Colmez and Nizioł) to coefficients arising from relative Fontaine-Laffaille modules of Faltings (on syntomic side) and relative Wach modules introduced by the speaker (on $(\varphi,\Gamma)$-module side).