arXiv subjects

Eivind Otto Hjelle

Publications and source records attributed to Eivind Otto Hjelle.

3 recordsLinked to original sources

arXiv2026

Functions on Irreducible Components of the Emerton-Gee Stack

Let $K / \mathbb{Q}_p$ be a finite unramified extension, and let $\mathcal{X}_n$ denote the Emerton-Gee stack parametrizing étale $(φ,Γ_K)$-modules of rank $n$. It is known since the work of Emerton-Gee that the irreducible components of the reduced special fiber of $\mathcal{X}$ are labeled by Serre weights $σ$ of $\operatorname{GL}_n(k)$. If such a component is denoted $\mathcal{X}(σ)$, we prove that $\mathcal{O}(\mathcal{X}(σ)) \cong \mathbb{F}[x_1,x_2,\dots,x_{n-1},x_n^{\pm 1}]$ when $σ$ is sufficiently generic.

math.NT↗

arXiv2025

The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups

We introduce and study the moduli stack $\mathcal{Y}$ of Breuil-Kisin modules with $\hat{G}$-structure and descent data, or Breuil-Kisin $(Γ,\hat{G})$-torsors for short. Specifically, for a dominant cocharacter $μ$, we define the moduli stack $\mathcal{Y}^{\leq μ}$ of Breuil-Kisin $(Γ,\hat{G})$-torsors with Hodge-Tate weights bounded by $μ$. We prove that $\mathcal{Y}^{\leq μ}$ is a $p$-adic formal algebraic stack, and show that it is smoothly equivalent to (the $p$-adic completion of) a twisted Schubert variety $\operatorname{Gr}^{\leq μ}_{\mathcal{G}}$ in the sense of Pappas-Zhu. This is a reformatted and lightly edited version of the author's PhD thesis, submitted to Northwestern University in August 2024.

math.NT↗

arXiv2016

Strong topologies for spaces of smooth maps with infinite-dimensional target

In this article we study two "strong" topologies for spaces of smooth functions from a finite-dimensional manifold to a (possibly infinite-dimensional) manifold modeled on a locally convex space. Namely, we construct Whitney type topologies for these spaces and a certain refinement corresponding to Michor's $\mathcal{FD}$-topology. Then we establish the continuity of certain mappings between spaces of smooth mappings, e.g.\ the continuity of the joint composition map. As a first application we prove that the bisection group of an arbitrary Lie groupoid (with finite-dimensional base) is a topological group (with respect to these topologies). For the reader's convenience the article includes also a proof of the folklore fact that the Whitney topologies defined via jet bundles coincide with the ones defined via local charts.

math.GN↗