Related papers: Clemens-Schmid exact sequence in characteristic p

For open and singular varieties in positive characteristic p we study the existence of an integral p-adic cohomology theory which is finitely generated, compatible with log crystalline cohomology and rationally compatible with rigid…

We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be…

We give examples of cohomological automorphic forms for unitary groups which are $p$-adically rigid.

Coclass theory can be used to define infinite families of finite p-groups of a fixed coclass. It is conjectured that the groups in one of these infinite families all have isomorphic mod-p cohomology rings. Here we prove that almost all…

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Beside a study of the general properties of such a cohomology, we show that, given a complex vector…

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.

The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth…

For each graph we construct graded cohomology groups whose graded Euler characteristic is the chromatic polynomial of the graph. We show the cohomology groups satisfy a long exact sequence which corresponds to the well-known…

We compare three different ways of defining group cohomology with coefficients in a crossed-module: 1) explicit approach via cocycles; 2) geometric approach via gerbes; 3) group theoretic approach via butterflies. We discuss the case where…

We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.

We compute the cohomology of the stack M_1 with coefficients in Z[1/2], and in low degrees with coefficients in Z. Cohomology classes on M_1 give rise to characteristic classes, cohomological invariants of families of curves of genus one.…

Groups with a non-cyclic Sylow $p$-subgroup have too many representations over a field of characteristic~$p$ to describe them fully. A~natural question arises, whether the world of representations coming from algebraic varieties with a…

In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…

We introduce a four-term long exact sequence that relates the cohomology of a smooth variety admitting a projective morphism onto a projective base to the cohomology of the open set obtained by removing the preimage of a general linear…

A curve over a perfect field $K$ of characteristic $p > 0$ is said to be superspecial if its Jacobian is isomorphic to a product of supersingular elliptic curves over the algebraic closure $\overline{K}$. In recent years, isomorphism…

Rump has recently showed the existence of a unique maximal Quillen exact structure on any additive category. We study when this is given by the stable short exact sequences, i.e. kernel-cokernel pairs consisting of a semi-stable kernel and…

We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in terms of dimension and total degree. We arrive at our example by…

We give necessary and sufficient inequalities for the existence of long exact sequences of m finite abelian p-groups with fixed isomorphy types. This problem is related to some generalized Littlewood-Richardson coefficients that we define…

Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.