Marvin Schneider | Search arXiv

arXiv2026

Universal norms of partially de Rham $B$-pairs and perfectness in Lubin--Tate Iwasawa theory

We study the behaviour of partially de Rham Selmer groups of $B$-pairs along abelian $p$-adic Lie extensions. In the cyclotomic case we compare them with the universal norms studied by Berger. For analytic Lubin--Tate $(φ,Γ)$-modules we prove that the $Ψ=1$ eigenspace is coadmissible of the expected rank over the algebra of analytic distributions and establish a comparison result between its Lie-algebra coinvariants and the projective limit of the partially de Rham Selmer groups of the attached $B$-pair.

math.NT↗

arXiv2024

A note on étale $(φ,Γ)$-modules in families

Let $Λ$ be a complete noetherian local ring with finite residue field of characteristic $p$ and $K/\mathbb{Q}_p$ a $p$-adic field. We show that, by deformation of the structure sheaf on the (transversal) prismatic site of a bounded $p$-adic formal scheme $\mathfrak{X}$, the category of prismatic $(Λ,F)$-crystals on $\mathfrak{X}$ is equivalent to $Λ$-étale local systems on the generic adic fiber of $\mathfrak{X}$ and that the cohomology of $(Λ,F)$-crystals recovers the pro-étale cohomology of the corresponding local systems. The proof follows the strategy used in \cite{bhatt2023prismatic} and \cite{marks2023prismatic}. From this we construct an isomorphism between Iwasawa cohomology of a $p$-adic Lie extension of $K$ and prismatic cohomology. Following \cite{wu2021galois}, we then reprove Dee's classical result \cite{article} on the equivalence between families of Galois representations and étale $(φ,Γ)$-modules.

math.NT↗