On Shimurian generalizations of the stack $BT_1\otimes F_p$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912162327298048 |
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| author | Drinfeld, Vladimir |
| author_facet | Drinfeld, Vladimir |
| contents | Let G be a smooth group scheme over $F_p$ equipped with a $G_m$-action such that all weights of $G_m$ on the Lie algebra of G are not greater than 1. Let $Disp_n^G$ be Eike Lau's stack of n-truncated G-displays (this is an algebraic stack over $F_p$). In the case n=1 we introduce an algebraic stack equipped with a morphism to $Disp_1^G$. 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 $G_m$ on GL(d).
We also discuss how to define an analog of the new stack for n>1 and how to replace $F_p$ by $Z/p^m Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11709 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Shimurian generalizations of the stack $BT_1\otimes F_p$ Drinfeld, Vladimir Algebraic Geometry Number Theory Representation Theory 14F30 Let G be a smooth group scheme over $F_p$ equipped with a $G_m$-action such that all weights of $G_m$ on the Lie algebra of G are not greater than 1. Let $Disp_n^G$ be Eike Lau's stack of n-truncated G-displays (this is an algebraic stack over $F_p$). In the case n=1 we introduce an algebraic stack equipped with a morphism to $Disp_1^G$. 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 $G_m$ on GL(d). We also discuss how to define an analog of the new stack for n>1 and how to replace $F_p$ by $Z/p^m Z$. |
| title | On Shimurian generalizations of the stack $BT_1\otimes F_p$ |
| topic | Algebraic Geometry Number Theory Representation Theory 14F30 |
| url | https://arxiv.org/abs/2304.11709 |