代数学コロキウム

過去の記録 ~12/09次回の予定今後の予定 12/10~

開催情報 水曜日 17:00~18:00 数理科学研究科棟(駒場) 056号室
担当者 今井 直毅, 三枝 洋一

2022年10月12日(水)

17:00-18:00   ハイブリッド開催
数理科学研究科所属以外の方は、オンラインでのご参加をお願いいたします。
Abhinandan 氏 (東京大学大学院数理科学研究科)
Syntomic complex with coefficients (English)
[ 講演概要 ]
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).