Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.11910 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913892408492032 |
|---|---|
| author | Hjelle, Eivind Otto |
| author_facet | Hjelle, Eivind Otto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups Hjelle, Eivind Otto Number Theory 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. |
| title | The Moduli Stack of Breuil-Kisin Modules with Descent Data for Reductive Groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.11910 |