Year: 2025
Type: preprint
Abstract: Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Let $π$ be an admissible smooth mod $p$ representation of $\mathrm{GL}_2(K)$ occurring in some Hecke eigenspaces of the mod $p$ cohomology and $\overline{r}$ be its underlying global two-dimensional Galois representation. When $\overline{r}$ satisfies some Taylor-Wiles hypotheses and is sufficiently generic at $p$, we compute explicitly certain constants appearing in the diagram associated to $π$, generalizing the results of Dotto-Le. As a result, we prove that the associated étale $(φ,\mathcal{O}_K^{\times})$-module $D_A(π)$ defined by Breuil-Herzig-Hu-Morra-Schraen is explicitly determined by the restriction of $\overline{r}$ to the decomposition group at $p$, generalizing the results of Breuil-Herzig-Hu-Morra-Schraen and the author.
Source: arXiv (Cornell University)
Author: Wang, Yitong
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415156344
Cites:
Cited by:
Related to: