Year: 2025
Type: article
Abstract: For an absolutely unramified extension L/\mathbb{Q}_{p} with imperfect residue field, we define and study Wach modules in the setting of (\varphi,\Gamma) -modules for L . Our main result establishes a direct equivalence between the category of lattices inside crystalline representations of the absolute Galois group of L and the category of integral Wach modules for L . Moreover, we provide a direct relation between a rational Wach module equipped with the Nygaard filtration and the filtered \varphi -module of its associated crystalline representation.
Source: Documenta Mathematica
DOI: 10.4171/dm/1015
Author: Abhinandan Abhinandan
Institution: Sorbonne Université
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413669633