2024/10/12 by Marquis, Nataniel
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2410.09483
Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give a general framework for these categories and the functors between them. We define the categories of étale projective S-modules over R to englobe categories that will correspond by Fontaine-type equivalences to finite free representations of a group. We study their preservation by base change, taking of invariants by a normal submonoid of S and coinduction to a bigger monoid. We define and study categories corresponding to finite type continuous representations over ℤp through the notions of finite projective (r,μ)-dévissage and of topological étale S-modules over R.