2024/10/12 by Marquis, Nataniel
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2410.09475
Let Δ be a finite set. We adapt the techniques of Carter-Kedlaya-Zábrádi to obtain a multivariable Fontaine equivalence which relates continuous finite dimensional \mathbbFq-representations of ∏α∈ Δ G_\mathbbFq( (X) ) to multivariable φ-modules over a \mathbbFq-algebra which is a domain. From this, we deduce a multivariable Lubin-Tate Fontaine equivalence for continuous finite type OK-representations of ∏α∈ Δ GK, where K|ℚp is a finite extension. We also obtain a plectic Fontaine equivalence and two equivalences for the subgroup GK,glec of the plectic Galois group.