On Shimurian Generalizations of the Stack $BT_1 \otimes\mathbb{F}_p$
Let $G$ be a smooth group scheme over $\mathbb{F}_p$ equipped with a $\mathbb{G}_m$-action such that all weights of $\mathbb{G}_m$ on $\textrm{Lie} (G)$ are $\le 1$. Let $\textrm{Disp}_n^G$ be Eike Lau's stack of $n$-truncated $G$-displays (this is an algebraic $\mathbb{F}_p$-stack). In the cas...
Saved in:
| Date: | 2025 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
|
| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1106 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
Institution
Journal of Mathematical Physics, Analysis, Geometry| Summary: | Let $G$ be a smooth group scheme over $\mathbb{F}_p$ equipped with a $\mathbb{G}_m$-action such that all weights of $\mathbb{G}_m$ on $\textrm{Lie} (G)$ are $\le 1$. Let $\textrm{Disp}_n^G$ be Eike Lau's stack of $n$-truncated $G$-displays (this is an algebraic $\mathbb{F}_p$-stack). In the case $n=1$ we introduce an algebraic stack equipped with a morphism to $\textrm{Disp}_1^G$. We conjecture that if $G=GL(d)$ then the new stack is canonically isomorphic to the reduction modulo $p$ of the stack of $1$-truncated Barsotti-Tate groups of height $d$ and dimension $d'$, where $d'$ depends on the action of $\mathbb{G}_m$ on $GL(d)$.
We also discuss how to define an analog of the new stack for $n>1$ and how to replace $\mathbb{F}_p$ by $\mathbb{Z}/p^m\mathbb{Z}$.
Mathematical Subject Classification 2020: 14F30 |
|---|