Syntomic complex with coefficients (Abhinandan, Université de Lille)

To prove crystalline comparison theorem, Fontaine and Messing utilized syntomic cohomology which is naturally related to crystalline cohomology. The key innovation in their paper was comparison between syntomic cohomology and p-adic étale cohomology via (Fontaine-Messing) period map, which eventually led to a complete proof of comparison theorem by Tsuji. Few years ago, Colmez-Nizioł gave an interpretation of (local version) Fontaine-Messing period map in terms of complexes of (\varphi, \Gamma)-modules and used it to prove the semistable comparison theorem for p-adic formal schemes. The goal of this talk is to generalize the local result of Colmez-Nizioł to an interesting class of coefficients, utilizing relative Wach modules introduced last week.