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...
Збережено в:
| Дата: | 2025 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1106 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | 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 |
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