Pith. sign in

REVIEW 3 cited by

On Shimurian generalizations of the stack $BT_1\otimes F_p$

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2304.11709 v4 pith:J4IMOBZE submitted 2023-04-23 math.AG math.NTmath.RT

Vladimir Drinfeld This is my paper · ORCID
classification math.AGmath.NTmath.RT
keywords stackactionalgebraicdispequippedalgebraanalogbarsotti-tate
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

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 $Z/p^m Z$.

Discussion (0). Continue with ORCID to comment.

Forward citations

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.

Pith tools