The Emerton-Gee stack of rank one (φ, Γ)-modules

Dat Pham (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We give a classification of rank one (φ, Γ)-modules with coefficients in a p-adically complete Zp-algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in arXiv:1908.07185, which gives an explicit description of the Emerton-Gee stack of (φ, Γ)-modules in the rank one case.

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Dat Pham. The Emerton-Gee stack of rank one (φ, Γ)-modules. 2022. ⟨hal-03884955⟩