Related papers: Purity of level m stratifications

We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is…

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected…

Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…

Let $Z'\subset \mathbb{P}^{n}$ be a smooth projective hypersurface of degree $d>1$ and let $Z\to \mathbb{P}^n$ be the $\mu_d$-cover totally ramified along $Z'$. We relate full level $d$ structures on the primitive cohomology $Z'$ with full…

Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on…

We give a value for the $F$-pure threshold at the maximal homogeneous ideal $\mathfrak{m}$ of the symmetric determinantal ring over a field of prime characteristic. The answer is characteristic independent, so we immediately get the log…

Let $X \hookrightarrow \overline{X}$ be an open immersion of smooth varieties over a field of characteristic $p>0$ such that the complement is a simple normal crossing divisor and let $\overline{Z} \subseteq Z \subseteq \overline{X}$ be…

Let $k$ be a field, $K/k$ finitely generated and $L/K$ a finite, separable extension. We show that the existence of a $k$-valuation on $L$ which ramifies in $L/K$ implies the existence of a normal model $X$ of $K$ and a prime divisor $D$ on…

In this paper we study the slope stratification on the good reduction of the type C family Shimura varieties. We show that there is an open dense subset $U$ of the moduli space such that any point in $U$ can be deformed to a point with a…

In this paper we study $\mathcal M(X)$, the set of diffeomorphism classes of smooth manifolds with the simple homotopy type of $X$, via a map $\Psi$ from $\mathcal M(X)$ into the quotient of $K(X)=[X,BSO]$ by the action of the group of…

A Kahler-type form is a symplectic form compatible with an integrable complex structure. Let M be either a torus or a K3-surface equipped with a Kahler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in M has…

We review the Newton stratification and Ekedahl-Oort stratification on the special fiber of a smooth integral model for a Shimura variety of Hodge type at a prime of good reduction. We show that the \mu-ordinary locus coincides with the…

We consider a closed Willmore surface properly immersed in ${\R}^m$ (m>2) with square-integrable second fundamental form, and with one point-singularity of finite arbitrary integer order. Using the "conservative" reformulation of the…

For a compact smooth manifold $M$ (with boundary) we prove that the topological rank of the diffeomorphism group Diff$_0^k(M)$ is finite for all $k\geq 1$. This extends a result from [2] where the same claim is proved in the special case of…

The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…

Given an n-dimensional variety Z with rational singularities, we conjecture that for a resolution of singularities whose reduced exceptional divisor E has simple normal crossings, the (n-1)-th higher direct image of the sheaf of…

In this paper we find, for any arbitrary finite topological type, a compact Riemann surface $\mathcal{M},$ an open domain $M\subset\mathcal{M}$ with the fixed topological type, and a conformal complete minimal immersion $X:M\to\R^3$ which…

We classify all the surfaces with p_g = q = 0 which admit an unramified covering which is isomorphic to a product of curves. Beyond the trivial case \PP^1 x \PP^1 we find 17 families which we explicitly describe. We reduce the problem to a…

We prove uniform boundedness statements for semistable pure sheaves on projective manifolds. For example, we prove that the set of isomorphism classes of pure sheaves of dimension 2 that are slope semistable with respect to ample classes…

A locally compact stable plane of positive topological dimension will be called semiaffine if for every line $L$ and every point $p$ not in $L$ there is at most one line passing through $p$ and disjoint from $L$. We show that then the plane…