Related papers: On a conjecture of Kashiwara

We present a result which can be used for stratifications with conical singularities to deduce that a perverse sheaf (in particular, an intersection homology sheaf) has reducible characteristic variety, given a hypothesis on the monodromy…

Let A be an abelian variety over a number field k. We show that weak approximation holds in the Weil-Ch\^atelet group of A/k but that it may fail when one restricts to the n-torsion subgroup. This failure is however relatively mild; we show…

For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient…

The Bloch-Beilinson-Murre conjectures predict the existence of a descending filtration on Chow groups of smooth projective varieties which is functorial with respect to the action of correspondences and whose graded parts depend solely on…

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. We prove the conjecture for type G_2, and…

Given a smooth quasi-projective complex algebraic variety $\mathcal{S}$, we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hypersurfaces over $\mathcal{S}$ of degree $d$ in…

In this work, we consider a finitely determined, quasihomogeneous, corank 1 map germ $f$ from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^3,0)$. We introduce the concept of the $\mu_{\mathbf{m},\mathbf{k}}$-minimal transverse slice of $f$}. Since…

The purpose of this note is to give a simple proof of the following theorem: Let $X$ be a normal projective variety over an algebraically closed field $k$, $\op{char} k = 0$ and let $D \subset X$ be a proper closed subvariety of $X$. Then…

Let \lambda be a partition of a positive integer n. Let C be a symmetric rigid tensor category over a field k of characteristic 0 or char(k)>n, and let V be an object of C. In our main result (Theorem 4.3) we introduce a finite set of…

Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…

Let $G$ be a smooth algebraic group over the field of rational functions of an excellent Dedekind scheme $S$ of equal characteristic $p>0.$ A N\'eron lft-model of $G$ is a smooth separated model $\mathscr{G} \to S$ of $G$ satisfying a…

This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras $E$ over a field $F$, such that $E \otimes_{F} E^{op}$ is semisimple. We assume that $E$…

We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…

The following conjecture on the deformation invariance of plurigenera is proved. For a smooth projective holomorphic family of compact complex manifolds over the open unit 1-disk such that all the fibers are of general type, every…

In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…

Let $k$ be a field and let $\Omega$ be a universal domain over $k$. Let $f:X \r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\leq 2$ such that the general…

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. Later V. Kac and the author proposed a…

Kottwitz conjectured a formula for the (semi-simple) trace of Frobenius on the nearby cycles for the local model of a Shimura variety with Iwahori-type level structure. In this paper, we prove his conjecture in the linear and symplectic…

We present simple conditions which guarantee a geometric convolution algebra to behave like a variant of the quasi-hereditary algebra. In particular, standard modules of the affine Hecke algebras of type $\mathsf{BC}$, and the quiver Schur…