Related papers: Local convolution of l-adic sheaves on the torus

In this paper we give an inherently toric description of a special class of sheaves (known as equivariant sheaves) over toric varieties, due in part to A. A. Klyachko. We apply this technology to heterotic compactifications, in particular…

This paper studies locally linear involutions on S^4. Our main theorem shows that any such involution with a 1-dimensional fixed-point set is necessarily linear, provided the fixed-point set admits an equivariant tubular neighborhood. The…

In this paper we prove a toric localization formula in cohomological Donaldson Thomas theory. Consider a -1-shifted symplectic algebraic space with a C* action leaving the -1-shifted symplectic form invariant. This includes the moduli space…

We the study of the monodromy of local systems with bounded ramification on a punctured disc defined over a non-archimedean valued field of characteristic zero. First, we construct the local Fourier transforms and we establish their main…

We prove that every $2$-local automorphism on a finite-dimensional semi-simple Lie algebra $\mathcal{L}$ over an algebraically closed field of characteristic zero is an automorphism. We also show that each finite-dimensional nilpotent Lie…

We conjecture that any perverse sheaf on a compact aspherical K\"ahler manifold has non-negative Euler characteristic. This extends the Singer-Hopf conjecture in the K\"ahler setting. We verify the stronger conjecture when the manifold X…

A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…

Let S be a K3 surface and Aut D(S) the group of auto-equivalences of the derived category of S. We construct a natural representation of Aut D(S) on the cohomology of all moduli spaces of stable sheaves (with primitive Mukai vectors) on S.…

Let \(E\) be a finite-dimensional real vector space. We study invertible objects in the monoidal category of constructible sheaves on \(E\), endowed with the convolution product \(\star\). We show that the inverse of an invertible…

We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasiprojective complex variety $X$ is integral. This answers…

We study the regularity of the conjugacy between an Anosov automorphism $L$ of a torus and its small perturbation. We assume that $L$ has no more than two eigenvalues of the same modulus and that $L^4$ is irreducible over $\mathbb Q$. We…

In this paper we study monodromy operators on moduli spaces $M_v(S,H)$ of sheaves on K3 surfaces with non-primitive Mukai vectors $v$. If we write $v=mw$, with $m>1$ and $w$ primitive, then our main result is that the inclusion $M_w(S,H)\to…

The goal of this paper is to motivate a boundedness conjecture on nearby slopes of $\ell$-adic sheaves in positive characteristic, and to prove it for smooth curves. For a constructible $\ell$-adic sheaf, we prove the finiteness of the set…

Firstly we show a generalization of the (1,1)-Lefschetz theorem for projective toric orbifolds and secondly we prove that on 2k-dimensional quasi-smooth hypersurfaces coming from quasi-smooth intersection surfaces, under the Cayley trick,…

We study the relation of the middle convolution to the $\ell$-adic Fourier transformation in the \'etale context. Using Katz' work and Laumon's theory of local Fourier transformations we obtain a detailed description of the local monodromy…

We determine precisely which irreducible hypergeometric sheaves have an extraspecial normalizer in characteristic 2 as their geometric monodromy groups. This resolves the last open case of the determination of local monodromy at 0 of…

In the present work we obtain rigidity results analysing the set of regular points, in the sense of Oseledec's Theorem. It is presented a study on the possibility of an Anosov diffeomorphisms having all Lyapunov exponents defined…

Local Fourier trnasforms, analogous to the $\ell$-adic Fourier transforms, are constructed for connections over $k((t))$. Following a program of Katz, a meromorphic connection on a curve is shown to be rigid, i.e. determined by local data…

Androulidakis and Skandalis showed how to associate a holonomy groupoid, a smooth convolution algebra and a C*-algebra to any singular foliation. In this note, we consider the singular foliations of a one-dimensional manifold given by…

We prove a global Torelli theorem for the moduli space of marked triples (X,m,A), consisting of an irreducible holomorphic symplectic manifold X, a marking m of its second integral cohomology, and a stable and rigid sheaf A of Azumaya…