On the Lau group scheme
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915619364929536 |
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| author | Drinfeld, Vladimir |
| author_facet | Drinfeld, Vladimir |
| contents | In a 2013 article, Eike Lau constructed a canonical morphism from the stack of $n$-truncated Barsotti-Tate groups over $F_p$ to the stack of $n$-truncated displays. He also proved that this morphism is a gerbe banded by a commutative group scheme. In this paper we describe the group scheme explicitly.
The stack of $n$-truncated Barsotti-Tate groups over $F_p$ has a generalization related to any pair $(G,μ)$, where $G$ is a smooth group scheme over $Z/p^n$ and $μ$ is a 1-bounded cocharacter of $G$. The same is true for the stack of $n$-truncated displays. We conjecture that in this more general situation the first stack is a gerbe over the second one banded by a commutative group scheme, and we give a conjectural description of this group scheme.
We also give a conjectural description of the stack of $n$-truncated Barsotti-Tate groups over the formal spectrum of $Z_p$ and of its $(G,μ)$-generalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06194 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Lau group scheme Drinfeld, Vladimir Algebraic Geometry 14L05, 14F30 In a 2013 article, Eike Lau constructed a canonical morphism from the stack of $n$-truncated Barsotti-Tate groups over $F_p$ to the stack of $n$-truncated displays. He also proved that this morphism is a gerbe banded by a commutative group scheme. In this paper we describe the group scheme explicitly. The stack of $n$-truncated Barsotti-Tate groups over $F_p$ has a generalization related to any pair $(G,μ)$, where $G$ is a smooth group scheme over $Z/p^n$ and $μ$ is a 1-bounded cocharacter of $G$. The same is true for the stack of $n$-truncated displays. We conjecture that in this more general situation the first stack is a gerbe over the second one banded by a commutative group scheme, and we give a conjectural description of this group scheme. We also give a conjectural description of the stack of $n$-truncated Barsotti-Tate groups over the formal spectrum of $Z_p$ and of its $(G,μ)$-generalization. |
| title | On the Lau group scheme |
| topic | Algebraic Geometry 14L05, 14F30 |
| url | https://arxiv.org/abs/2307.06194 |