arXiv subjects

John Enns

Publications and source records attributed to John Enns.

3 recordsLinked to original sources

arXiv2023

Mod $p$ local-global compatibility for $\mathrm{GSp}_4(\mathbb{Q}_p)$ in the ordinary case

Let $F$ be a totally real field of even degree in which $p$ splits completely. Let $\overline{r}:G_F \rightarrow \mathrm{GSp}_4(\overline{\mathbb{F}}_p)$ be a modular Galois representation unramified at all finite places away from $p$ and upper-triangular, maximally nonsplit, and of parallel weight at places dividing $p$. Fix a place $w$ dividing $p$. Assuming certain genericity conditions and Taylor--Wiles assumptions, we prove that the $\mathrm{GSp}_4(F_w)$-action on the corresponding Hecke-isotypic part of the space of mod $p$ automorphic forms on a compact mod center form of $\mathrm{GSp}_4$ with infinite level at $w$ determines $\overline{r}|_{G_{F_w}}$.

math.NT↗

arXiv2018

Multiplicities in the ordinary part of mod $p$ cohomology for $\mathrm{GL}_n(\mathbb{Q}_p)$

Given a continuous ordinary Galois representation $\barρ:G_{\mathbb{Q}_p}\rightarrow\mathrm{GL}_n(\overline{\mathbb{F}}_p)$, Breuil and Herzig constructed an admissible smooth $\overline{\mathbb{F}}_p$-representation $Π(\barρ)^{\mathrm{ord}}$ of $\mathrm{GL}_n(\mathbb{Q}_p)$ and showed that it occurs in certain globally defined mod $p$ cohomology spaces. By applying Taylor-Wiles patching to spaces of ordinary automorphic representations we prove that the indecomposable pieces of $Π(\barρ)^{\mathrm{ord}}$ each occur with the same multiplicity at a well-chosen tame level.

math.NT↗

arXiv2018

On weight elimination for $\mathrm{GL}_n(\mathbb{Q}_{p^f})$

We show that the modular Serre weights of a sufficiently generic mod $p$ Galois representation of an unramified $p$-adic field are themselves generic, and give precise bounds on the genericity, by extending previous work of Emerton, Gee and Herzig. Our bounds are nearly optimal in some cases. We use this to improve recent weight elimination theorems.

math.NT↗