On Shimurian generalizations of the stack $BT_1\otimes F_p$
| Autor: | Drinfeld, Vladimir |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $Z/p^m Z$. Comment: Added Appendix D and references to some recent works |
| Databáze: | arXiv |
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