Related papers: Normality of monodromy group in generic convolutio…

Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…

Let S be a K3 surface. In part I of this paper, we constructed a representation of the group Aut D(S), of auto-equivalences of the derived category of S. We interpreted this infinite dimensional representation, as the natural action of Aut…

Let K be a global field, let S be a finite set of primes of K containing the archimedean primes and let A be an abelian variety over K. We generalize the duality theorem established in our paper "On Neron class groups of abelian varieties"…

We associate to every positive braid a braid monodromy group, generalizing the geometric monodromy group of an isolated plane curve singularity. If the closure of the braid is a knot, we identify the corresponding group with a framed…

Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's…

Let X be a smooth complex projective variety. The group of autoequivalences of the derived category of X acts naturally on its singular cohomology H(X, Q) and we denote by Geq(X) the Zariski closure of its image in Gl(H(X, Q)). We study the…

Given a relative faithfully flat pointed scheme over the spectrum of a discrete valuation ring $X \to S$ this paper is motivated by the study of the natural morphism from the fundamental group scheme of the generic fiber $X_\eta $ to the…

The Griffiths group $\Gr^r(X)$ of a smooth projective variety $X$ over an algebraically closed field is defined to be the group of homologically trivial algebraic cycles of codimension $r$ on $X$ modulo the subgroup of algebraically trivial…

This article studies a confluence of a pair of regular singular points to an irregular one in a generic family of time-dependent Hamiltonian systems in dimension 2. This is a general setting for the understanding of the degeneration of the…

Let $E$ be an abelian scheme over a geometrically connected variety $X$ defined over $k$, a finitely generated field over $\mathbb{Q}$. Let $\eta$ be the generic point of $X$ and $x\in X$ a closed point. If $\mathfrak{g}_l$ and…

We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing $t$-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories…

Let X be a smooth, geometrically connected variety over a p-adic local field. We show that the pro-unipotent fundamental group of X (in both the etale and crystalline settings) satisfies the weight-monodromy conjecture, following…

We classify all normal Schubert varieties in the affine Grassmannian of a semisimple group over an arbitrary field with special attention to small positive characteristic. The proof is elementary and relies on tangent space calculations for…

Let $pi:X\to\Delta$ be a one-parameter degeneration whose central fiber $X_0$ has a single ordinary double point. The nearby- and vanishing-cycle formalism determines a canonical perverse sheaf on $X_0$, obtained from the variation morphism…

The Shafarevich-Tate group $W (\mathscr{A})$ measures the failure of the Hasse principle for an abelian variety $\mathscr{A}$. Using a correspondence between the abelian varieties and the higher dimensional non-commutative tori, we prove…

For each nonnegative integer $g$, we classify the ramification types and monodromy groups of indecomposable coverings of complex curves $f: X\to Y$ where $X$ has genus $g$, under the hypothesis that $n:=\deg(f)$ is sufficiently large and…

A certain "condition (S)" on reductive algebraic groups was introduced in [GT2], in which a slightly stronger condition (S+) was shown to have very strong consequences. We show that a wide class of Kloosterman and hypergeometric sheaves…

We relate Nakajima Quiver Varieties (or, rather, their multiplicative version) with moduli spaces of perverse sheaves. More precisely, we consider a generalization of the concept of perverse sheaves: microlocal sheaves on a nodal curve X.…

Let X be a smooth affine algebraic variety over a field K of characteristic 0, and let R be a complete parameter K-algebra (e.g. R = K[[h]]). We consider associative (resp. Poisson) R-deformations of the structure sheaf O_X. The set of…

RR fluxes representing different cohomology classes may correspond to the same twisted K-theory class. We argue that such fluxes are related by monodromies, generalizing and sometimes T-dual to the familiar monodromies of a D7-brane. A…