Related papers: A Class of Incomplete Character Sums

These notes aim to give a first introduction to intersection cohomology and perverse sheaves with applications to representation theory or quantum groups in mind.

We study sums over primes of trace functions of $\ell$-adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of…

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg's type II classical graded Lie algebras.

In this note, we show various versions of holomorphic Morse inequalities tensoring with a coherent sheaf.

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.

We show that in positive characteristic special loci of deformation spaces of rank one $\ell$-adic local systems are quasilinear. From this we deduce the Hard Lefschetz theorem for rank one $\ell$-adic local systems and a generic vanishing…

I present a generalized notion of obstruction in \v{C}ech cohomology on semi-modules, which allows one to characterize non-disturbing contextual behaviors with any semi-field. This framework generalizes the usual \v{C}ech cohomology used in…

We classify the nonsplit extensions of elementary abelian $p$-groups by $PSL_2(q)$, with odd $p$ dividing $q-1$, for an irreducible induced action, calculate the relevant low-dimensional cohomology groups, and describe the automorphism…

In studying the Bott-Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott-Chern q-complete manifolds.

For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we…

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…

We prove a vanishing theorem for the p-adic cohomology of exponential sums on affine space. In particular, we obtain new classes of exponential sums on affine space that have a single nonvanishing p-adic cohomology group. The dimension of…

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…

We study Chevalley-Eilenberg cohomology of physically relevant Lie superalgebras related to supersymmetric theories, providing explicit expressions for their cocycles in terms of their Maurer-Cartan forms. We then include integral forms in…

We extend the definition of the unramified curve-tame cohomology groups to $\mathbb{A}^1$-invariant \'etale sheaves under some additional hypotheses. We define a pairing of this group with the Suslin homology satisfying desirable properties…

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…

We generalise the notion of a Barge-Diamond complex, in the one-dimensional case, to a mixed system of tiling substitutions. This gives a way of describing the associated tiling space as an inverse limit of Barge-Diamond complexes. We give…

We study parabolic induction producing $\ell$-adic sheaves on a parahoric subgroup scheme in the loop group of a reductive group. Under a genericity assumption on the input data, we prove that it produces conjugation equivariant perverse…

We consider character sums determined by isogenies of elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies, and produce explicit formulas for isogenies of small…