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On the Lau group scheme

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arxiv 2307.06194 v9 pith:6VIC5TLV submitted 2023-07-12 math.AG

classification math.AG
keywords groupschemestacktruncatedbarsotti-tategroupsbandedcommutative
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

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 $(G,\mu)$, where $G$ is a smooth group scheme over $Z/p^n$ and $\mu$ 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 $(G,\mu)$-generalization.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sheared displays and $p$-divisible groups

    math.NT 2026-01 conditional novelty 8.0 of 10

    Over p-nilpotent rings, p-divisible groups are equivalent to sheared displays, resolving Drinfeld's conjecture and giving a Dieudonné theory for all p-divisible groups.

  2. The Shimurian BT stack is a gerbe over truncated displays

    math.AG 2025-10 accept novelty 7.0 of 10

    The mod p Shimurian BT stack is a gerbe over the stack of truncated displays, confirming Drinfeld's gerbe conjecture.

  3. Ring stacks conjecturally related to the stacks $BT_n^{G,\mu}$

    math.AG 2025-10 conditional novelty 6.0 of 10

    This paper defines the ring stacks sRn and sR⊕n from the ring space of sheared Witt vectors and builds several explicit quasi-isomorphic models for them.

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