arXiv subjects

Qijun Yan

Publications and source records attributed to Qijun Yan.

4 recordsLinked to original sources

arXiv2025

On certain integral Frobenius period maps for Shimura varieties and their reductions

We formulate an integral Frobenius period map for the framed crystalline prismatization of the $p$-integral model $\mathcal{S}$ of a Shimura variety with good reduction. By analyzing reductions of this map, we derive a period map from the mod $p$ fiber $S$ of $\mathcal{S}$ to the moduli stack of 1-1 truncated local $G$-shtukas in the prismatic topology, which refines the zip period map of $S$ within this topology. Furthermore, we show that the pair $(\mathcal{S}, S)$ is associated with a double $G$-zip. Additionally, we introduce a framework of base reduction diagrams.

math.AG↗

arXiv2023

A relation between zip stacks and moduli stacks of truncated local shtukas

Let $G$ be a reductive group over a field $k$, and let $\mu$ be a cocharacter of $G$. We prove that Viehmann's double coset spaces associated with $(G, \mu)$ are representable by certain Lusztig varieties, and establish a similar result for the mixed characteristic case. This representability enables a comparison between the moduli stacks of truncated local shtukas and zip stacks. Over a perfect field of positive characteristic, we establish a homeomorphism between the coarse moduli stack of $1\text{-}1$-truncated local $G$-shtukas and that of $G$-zips, thereby enriching our understanding of zip period maps in the context of Shimura varieties.

math.AG↗

arXiv2021

An alternative construction of zip period maps for Shimura varieties

Let $S$ be the special fibre of a Shimura variety of Hodge type, with good reduction at a place above $p$. We give an alternative construction of the zip period map for $S$, which is used to define the Ekedahl-Oort strata of $S$. The method employed is local, $p$-adic, and group-theoretic in nature.

math.AG↗

arXiv2018

Ekedahl-Oort stratifications of Shimura varieties via Breuil-Kisin windows

Let $ S $ be the special fibre of the good reduction of a Shimura variety of Hodge type. By constructing adapted deformations for the associated $p$-divisible groups of $ S $, we manage to construct a morphism from $S$ to some quotient sheaf of the loop group associated with $S$. We show that the geometric fibres of this morphism give back the Ekedahl-Oort strata of $S$. For any geometric point $ x $ of $ S $, we give a deformation over $ W(k(x)) $ of the $ p $-divisible group associated with $ x $ by (non-canonically) constructing a Breuil-Kisin window (which corresponds to a $ p $-divisible group over $ W(k(x)) $ by the work of Kisin). This map in a sense gives a conceptual interpretation of Viehmann's new invariants "truncations of level one of elements in the loop group".

math.AG↗