Related papers: Central leaves in loop groups

Kisin and Pappas constructed integral models of Hodge-type Shimura varieties with parahoric level structure at $p>2$, such that the formal neighbourhood of a mod~$p$ point can be interpreted as a deformation space of $p$-divisible group…

Consider all moduli points corresponding with polarized abelian varieties in characteristic p such that the associated quasi-polarized p-divisible group is geometrically isomorphic with a given one. This defines a subset C of the moduli…

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that…

Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the…

We discuss various problems regarding the structure of the foliation of some foliated submanifolds S of C^n, in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates),…

This paper generalizes the classical theory of Newton polygons from the case of general linear groups to the case of split reductive groups. It also gives a root-theoretic formula for dimensions of Newton strata in the adjoint quotients of…

In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…

We investigate the geometry of the special fiber of the integral model of a Shimura variety with parahoric level at a given prime place. To be more precise, we deal with the definition of central leaves in this situation, their local…

In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The…

We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.

Although little can be gleaned about a loop with the property that its squares are, say, left nuclear ($xx\cdot yz = (xx\cdot y)z$), if its squares are also, say, middle nuclear ($(x\cdot yy)z = x(yy\cdot z)$), then the loop exhibits more…

This is a collection of articles, written as sections, on arithmetic properties of differential equations, holomorphic foliations, Gauss-Manin connections and Hodge loci. Each section is independent from the others and it has its own…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…

The Newton strata of a reductive $p$-adic group are introduced in \cite{Newton} and play some role in the representation theory of $p$-adic groups. In this paper, we give a geometric interpretation of the Newton strata.

We generalize the notion of Ekedahl-Oort strata to elements in the loop group of any connected reductive group, and call the resulting discrete invariant the truncation of level 1 of the element. We give conditions for the Newton points…

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis…

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…

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…

Isotopes of C-loops with unique non-identity squares are shown to be both C-loops and A-loops. The relationship between C-loops and Steiner loops is further studied. Central loops with the weak and cross inverse properties are also…

We classify singular foliations admitting a given leaf and a given transverse singular foliation.