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Number Theory Seminar
Seminar information archive ～06/09｜Next seminar｜Future seminars 06/10～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2024/06/19
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Abhinandan (University of Tokyo)
Prismatic F-crystals and Wach modules (English)
Abhinandan (University of Tokyo)
Prismatic F-crystals and Wach modules (English)
[ Abstract ]
For an absolutely unramified extension K/Qp with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of GK (the absolute Galois group of K). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of GK are equivalent to the category of prismatic F-crystals on the absolute prismatic site of OK, the ring of integers of K. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic F-crystals over the absolute prismatic site of OK. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
For an absolutely unramified extension K/Qp with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of GK (the absolute Galois group of K). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of GK are equivalent to the category of prismatic F-crystals on the absolute prismatic site of OK, the ring of integers of K. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic F-crystals over the absolute prismatic site of OK. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
