相关论文: An alternative construction of zip period maps for…

We define quotient stacks of "zip flags". They form towers above the stack of $G$-zips introduced by Moonen, Pink, Wedhorn and Ziegler. We define a stratification on the stack of zip flags, and prove that it is principally pure, under a…

We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of…

We investigate the bad reduction of certain Shimura varieties (associated to the symplectic group). More precisely, we look at a model of the Shimura variety at a prime p, with parahoric level structure at p. We show that this model is…

For a connected reductive group $G$ over a finite field, we define partial Hasse invariants on the stack of $G$-zip flags. We obtain similar sections on the flag space of Shimura varieties of Hodge-type. They are mod $p$ automorphic forms…

When $p$ is inert in the quadratic imaginary field $E$ and $m<n$, unitary Shimura varieties of signature $(n,m)$ and a hyperspecial level subgroup at $p$, carry a natural foliation of height 1 and rank $m^2$ in the tangent bundle of their…

This paper is a continuation of our paper math.AG/0006222. We study the reduction of certain PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good"…

For a Shimura variety of Hodge type with hyperspecial level at a prime $p$, the Newton stratification on its special fiber at $p$ is a stratification defined in terms of the isomorphism class of the Dieudonne module of parameterized abelian…

Let $P$ be the image of a period map. We discuss progress towards a conjectural Hodge theoretic completion $\overline{P}$, an analogue of the Satake-Baily-Borel compactification in the classical case. The set $\overline{P}$ is defined and…

The main result of this paper is the construction of a new class of weight shifting operators, similar to the theta operators of arXiv:1902.10911, arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata of the…

We study local models that describe the singularities of Shimura varieties of non-PEL type for orthogonal groups at primes where the level subgroup is given by the stabilizer of a single lattice. In particular, we use the Pappas-Zhu…

This is a survey article that advertizes the idea that there should exist a theory of p-adic local analogues of Shimura varieties. Prime examples are the towers of rigid-analytic spaces defined by Rapoport-Zink spaces, and we also review…

We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…

For a linear algebraic group $G$ over $\mathbf Q$, we consider the period domains $D$ classifying $G$-mixed Hodge structures, and construct the extended period domains $D_{\Sigma}$. In particular, we give toroidal partial compactifications…

For a point $x_0$ in a Shimura variety attached to a Shimura datum of Hodge type $(G,X)$, we have an associated abelian scheme $A_0$. Fixing a non-empty finite set $\mathcal{S}$ of primes, we consider the simultaneous supersingular…

We give an expository overview over recent results on the global structure and geometry of the Newton stratification of the reduction modulo p of Shimura varieties of Hodge type with hyperspecial level structure. More precisely, we discuss…

In this paper, we give a geometric construction of the Jacquet-Langlands transfer for automorphic forms of higher weights by studying the geometry of the mod $p$ fibres of different Hodge type Shimura varieties which satisfy a mild…

We study the mod $p$-points of the Kisin--Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point, proving a…

Let $X$ be the special fiber of a unitary Shimura variety of hyperspecial level at a prime $p$ inert in the totally real field $F$. Let $Y\to X$ be the associated flag space. For every $L$-dominant weight $\lambda$, let…

We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…

Let (P,X) be Shimura data, M=M(P,X,K) the Shimura variety of level K. To an algebraic representation of P, one can associate a mixed sheaf (variation of Hodge structure, l-adic sheaf) on M. In the paper, we study the degeneration of such…