arXiv subjects

Ali Partofard

Publications and source records attributed to Ali Partofard.

3 recordsLinked to original sources

arXiv2025

Igusa Stack for some exceptional Shimura Varieties

We study the integral models of meta-unitary Shimura varieties through the lens of Scholze's fiber product conjecture. Reformulating Bultel's original construction in terms of moduli stacks of Shtukas and Igusa stacks, we prove the validity of the fiber product formula for this class of non-abelian type Shimura varieties, thereby generalizing the works of Zhang and Daniels, Van Hoften, Kim, and Zhang. We utilize this geometric description to derive local-global compatibility results and, adapting the strategy of Zhu and Yang, apply the unipotent categorical local Langlands correspondence to prove a general vanishing theorem for the generic part of the cohomology of meta-unitary Shimura varieties.

math.AG↗

arXiv2025

Embeddings of Certain Exceptional Shimura Varieties into Siegel Modular Varieties

We define a class of local Shimura varieties that contains some local Shimura varieties for exceptional groups, and for this class, we construct a functor from $\left(G, \mu\right)$-displays to $p$-divisible groups. As an application, we prove that for this class, the local Shimura variety is representable and perfectoid at the infinite level. Considering the global counterpart of this class, we embed certain exceptional Shimura varieties into Siegel modular varieties. In particular, we prove that they are perfectoid at the infinite level.

math.AG↗

arXiv2024

Deformations of Prismatic Higher $(G,\mu)$-Displays over Quasi-Syntomic Rings

We prove a deformation theorem for prismatic higher $(G,\mu)$-displays over quasi-syntomic rings. As an application, we extend the classification of $p$-divisible groups via prismatic Dieudonn\'e modules to a class of rings, properly containing quasi-syntomic rings. Finally, we relate the stack of prismatic higher $(G,\mu)$-displays to integral local Shimura varieties.

math.NT↗