$(G,\mu)$-Windows and Deformations of $(G,\mu)$-Displays

Mohammad Hadi Hedayatzadeh; Oliver Bueltel

$(G,\mu)$-Windows and Deformations of $(G,\mu)$-Displays

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arxiv 2011.09163 v1 pith:FN4ZLOCL submitted 2020-11-18 math.NT math.AG

Oliver Bueltel , Mohammad Hadi Hedayatzadeh This is my paper · ORCID

classification math.NTmath.AG

keywords windowsdisplaysgroupoidadjointaffinecharacteristiccocharacterdeformations

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abstract

Let $k_0$ be a finite field of characteristic $p$, let $G$ be a smooth affine group scheme over $\mathbb{Z}_p$, and let $\mu$ be a cocharacter of $G_{W(k_0)}$ such that the set of $\mu$-weights of $\text{Lie}\, G$ is a subset of $\{-1,0,1,2,\dots\}$. We prove that the groupoid of adjoint nilpotent $(G,\mu)$-displays is equivalent to the groupoid of $(G,\mu)$-windows, which are the generalizations of windows.

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Moduli of truncated shtukas and displays
math.AG 2025-06 conditional novelty 6.0 of 10

Truncated shtukas and displays are classified by quotient stacks of loop groups by display groups, with explicit cutoff bounds N0 = 2C+1 beyond which truncation determines the full object.

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