l-Adic Étale Cohomology of PEL Type Shimura Varieties with Non-Trivial Coefficients

Given a Shimura datum (G, h) of PEL type, let p be an odd prime at which G is unramified. In [13], we established a formula computing the l-adic cohomology of the associated Shimura varieties (regarded as a representation of the acidic points of G and of the local Weil group at p) in terms of that of their local models at p (the associated Rapoport-Zink spaces) and of the corresponding Igusa varieties. In this paper we extend those results (which are for cohomology with constant l-adic coefficients) to the general case of coefficients in a lisse étale sheaf attached to a finite dimensional l-adic representation of the group G

On the cohomology of certain PEL-type Shimura varieties

In this article we study the local geometry at a prime p of PEL-type Shimura varieties for which there is a hyperspecial level subgroup. We consider the Newton polygon stratification of the special fiber at p of Shimura varieties and show that each Newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding PEL-type Rapoport-Zink spaces with certain smooth varieties (which we call Igusa varieties) and of the action on them of a p-adic group that depends on the stratum. We then extend our construction to characteristic zero and, in the case of bad reduction at p, use it to compare the vanishing cycle sheaves of the Shimura varieties to those of the Rapoport-Zink spaces. As a result of this analysis, in the case of proper Shimura varieties we obtain a description of the l-adic cohomology of the Shimura varieties in terms of the l-adic cohomology with compact supports of the Igusa varieties and of the Rapoport-Zink spaces for any prime l≠p

On the Hodge–Newton filtration for p-divisible O-modules

The notions Hodge–Newton decomposition and Hodge–Newton filtration for F-crystals are due to Katz and generalize Messing’s result on the existence of the local-étale filtration for p-divisible groups. Recently, some of Katz’s classical results have been generalized by Kottwitz to the context of F-crystals with additional structures and by Moonen to μ-ordinary p-divisible groups. In this paper, we discuss further generalizations to the situation of crystals in characteristic p and of p-divisible groups with additional structure by endomorphisms

Abelian covers of P1\mathbb{P}^1 of pp-ordinary Ekedahl-Oort type

Given a family of abelian covers of $\mathbb{P}^1$ and a prime $p$ of good reduction, by considering the associated Deligne--Mostow Shimura variety, we obtain lower bounds for the Ekedahl-Oort type, and the Newton polygon, at $p$ of the curves in the family. In this paper, we investigate whether such lower bounds are sharp. In particular, we prove sharpness when the number of branching points is at most five and $p$ sufficiently large. Our result is a generalization under stricter assumptions of [1, Theorem 6.1] by Bouw, which proves the analogous statement for the $p$-rank, and it relies on the notion of Hasse-Witt triple introduced by Moonen in [2]

On Non-Basic Rapoport-Zink Spaces

In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz's prediction that thir l-adic cohomology groups provide a realization of certain cases of local Laglands correspondences and in particular to the question of whether they contain any supercuspidal representations. Our results are compatible with this prediction and identify many cases when no supercuspidal representations appear. In those cases we prove that the l-adic cohomology of some associated lower-dimensional (and in most favorable cases basic) Rapoport-Zink spaces. Such an equality was originally conjectured by Harris in [11](Conjecture 5.2, p.420)

On certain unitary group Shimura varieties. Variétés de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales

In this paper, we study the local geometry at a prime p of a certain class of (PEL) type Shimura varieties. We begin by studying the Newton polygon stratification of the special fiber of a Shimura variety with good reduction at p. Each stratum can be described in terms of the products of the reduced fiber of the corresponding Rapoport-Zink space with some smooth varieties (we call the Igusa varieties), and of the action on them of a certain p-adic group T_α, which depends on the stratum. (The definition of the Igusa varieties in this context is based upon a result of Zink on the slope filtration of a Barsotti-Tate group and on the notion of Oort’s foliation.) In particular, we show that it is possible to compute the étale cohomology with compact supports of the Newton polygon strata, in terms of the étale cohomology with compact supports of the Igusa varieties and the Rapoport-Zink spaces, and of the group homology of T_α. Further more, we are able to extend Zariski locally the above constructions to characteristic zero and obtain an analoguous description for the étale cohomology of the Shimura varieties in both the cases of good and bad reduction at p. As a result of this analysis, we obtain a description of the l-adic cohomology of the Shimura varieties, in terms of the l-adic cohomology with compact supports of the Igusa varieties and of the Rapoport-Zink spaces

STUDI HABITAT BADAK SUMATERA (DICERORHINUS SUMATRENSIS)DI KAWASAN HUTAN SAMARKILANG KAWASAN EKOSISTEM LEUSER

Banda Ace