Related papers: Purity of level m stratifications

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first…

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM field, proving conjectures of Ash and…

Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of "parity sheaves", which are objects in the constructible derived category of sheaves with coefficients in…

We prove that group homology of the diffeomorphism group of $\#^g S^n \times S^n$ as a discrete group is independent of $g$ in a range, provided that $n>2$. This answers the high dimensional version of a question posed by Morita about…

We supply a proof of the fact that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics is topologically tame. This proves the Marden's conjecture. Our approach is to form an exhaustion $M_i$ of $M$…

The density property for a Stein manifold X implies that the group of holomorphic diffeomorphisms of X is infinite-dimensional and, in a certain well-defined sense, as large as possible. We prove that if G is a complex semisimple Lie group…

Given a sufficiently positive embedding $X\subset\mathbb{P}^N$ of a smooth projective variety $X$, we consider its secant variety $\Sigma$ that comes equipped with the embedding $\Sigma\subset\mathbb{P}^N$ by its construction. In this…

Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1. For a subset X of M denote by D(M,X) the group of diffeomorphisms of M fixed on X. In this note we consider a special class F of smooth maps…

In this note, we use estimates given in the recent preprint [Her11b]to deduce a formula for the F-pure threshold of a binomial hypersurface over a field of prime characteristic. These formulas are given in terms of the associated splitting…

In this note we prove that if $S$ is an affine non-toric $\mathbb{G}_m$-surface of hyperbolic type that admits a $\mathbb{G}_a$-action and $X$ is an affine irreducible variety such that $Aut(X)$ is isomorphic to $Aut(S)$ as an abstract…

In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity…

Fix a scheme $S$ of characteristic $p$. Let $\mathscr{M}$ be an $S$-algebraic stack and let $\mbox{Fdiv}(\mathscr{M})$ be the stack of $\mbox{F}$-divided objects, that is sequences of objects $x_i\in\mathscr{M}$ with isomorphisms…

This paper is a continuation of [G-dS1]. We study foliations of two types on Shimura varieties $S$ in characteristic $p$. The first, which we call "tautological foliations", are defined on Hilbert modular varieties, and lift to…

In this paper we study the topology of the space of Riemann surfaces in a simply connected space X, S_{g,n} (X, \gamma). This is the space consisting of triples, (F_{g,n}, \phi, f), where F_{g,n} is a Riemann surface of genus g and…

Let $p$ be a branched covering of a Riemann surface to the Riemann sphere $\mathbb{P}^1$, with branching set $B \subset \mathbb{P}^1$. We define the complexity of $p$ as infinity, if $\mathbb{P}^1 \setminus B$ does not admit a hyperbolic…

Let $\mathcal{O}_K$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with perfect residue field. We prove the existence of the Hodge-Newton filtration for $p$-divisible groups over $\mathcal{O}_K$ with additional…

We show that a complete $m$-dimensional immersed submanifold $M$ of $\mathbb{R}^{n}$ with $a(M)<1$ is properly immersed and have finite topology, where $a(M)\in [0,\infty]$ is an scaling invariant number that gives the rate that the norm of…

For every adic space $Z$ we construct a site $Z_t$, the tame site of $Z$. For a scheme $X$ over a base scheme $S$ we obtain a tame site by associating with $X/S$ an adic space $\textit{Spa}(X,S)$ and considering the tame site…

A complex algebraic surface $S$ is a $\mathbb{Q}$-homology plane if $H_{i}(S,\mathbb{Q})=0$ for $i>0$. The Negativity Conjecture of Palka asserts that $\kappa(K_{X}+\tfrac{1}{2}D)=-\infty$, where $(X,D)$ is a log smooth completion of $S$.…

For Shimura varieties of Hodge type, we show that there are natural isomorphisms between locally analytic complete cohomology groups and cohomology groups for flag varieties with coefficient which is given by their perfectoid covers. This…