arXiv subjects

Mohammad Hadi Hedayatzadeh

Publications and source records attributed to Mohammad Hadi Hedayatzadeh.

7 recordsLinked to original sources

arXiv2026

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 $\left(G, μ\right)$-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↗

arXiv2026

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

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

math.NT↗

arXiv2020

$(G,μ)$-Windows and Deformations of $(G,μ)$-Displays

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

math.NT↗

arXiv2019

On Certain Morphisms between Flag Varieties

The aim of this paper is to construct certain closed embeddings of Grassmannian varieties, using tensor operations on vector bundles. These embeddings generalize Segre and Plücker morphisms.

math.AG↗

arXiv2019

A Cartesian Diagram of Rapoport-Zink Towers over Universal Covers of $p$-Divisible Groups

In their paper Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours to compute certain non-trivial $\ell$-adic étale cohomology classes appearing in the the generic fiber of Lubin-Tate and Rapoprt-Zink towers. We also study the behavior of the vector bundle functor on the fundamental curve in $p$-adic Hodge theory, defined by Fargues-Fontaine, under multilinear morphisms.

math.NT↗

arXiv2019

Tensor Operations on Group Schemes

In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would naturally expect.

math.NT↗

arXiv2010

Exterior Powers of Barsotti-Tate Groups

Let $ \CO $ be the ring of integers of a non-Archimedean local field and $ π$ a fixed uniformizer of $ \CO $. We establish three main results. The first one states that the exterior powers of a $ π$-divisible $ \CO $-module scheme of dimension at most 1 over a field exist and commute with algebraic field extensions. The second one states that the exterior powers of a $p$-divisible group of dimension at most 1 over arbitrary base exist and commute with arbitrary base change. The third one states that when $ \CO $ has characteristic zero, then the exterior powers of $ π$-divisible groups with scalar $ \CO $-action and dimension at most 1 over a locally Noetherian base scheme exist and commute with arbitrary base change. We also calculate the height and dimension of the exterior powers in terms of the height of the given $p$-divisible group or $ π$-divisible $ \CO $-module scheme.

math.NT↗