北大数論セミナー：Crystalline representations, Wach modules and prismatic F-crystals

Time： 10:30 – 11:30

Place：理学部3号館3-205室　　　

Speaker：Abhinandan 氏（東京大学）

Title： Crystalline representations, Wach modules and prismatic F-crystals

Abstract：For an absolutely unramified extension $K/\mathbb{Q}_p$ 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 $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, 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 $O_K$. If time permits, we will also mention a generalisation of these results to the case of a “small” base ring.

Organizer：安田 正大