Related papers: Sur une conjecture de Kottwitz au bord
This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces. We cover compactification of Siegel modular varieties;…
In this paper we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the results given in the literature.
We compute the integral cohomology of the minimal non-trivial nilpotent orbit in a complex simple (or quasi-simple) Lie algebra. We find by a uniform approach that the middle cohomology group is isomorphic to the fundamental group of the…
The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various…
In this paper, we introduce and study the notion of linkage of modules by reflexive homomorphisms. This notion unifies and generalizes several known concepts of linkage of modules and enables us to study the theory of linkage of modules…
We give a complete description of the potential failure of the surjectivity of the Thom morphism from complex cobordism to integral cohomology for compact Lie groups via a detailed study of the Atiyah-Hirzebruch spectral sequence and the…
We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Associated with each cohomology is a primitive cohomology…
We study Hodge bundles on Siegel varieties and their various extensions to smooth toroidal compactifications. Precisely, we construct a canonical Hodge bundle on an arbitrary Siegel variety so that the holomorphic tangent bundle can be…
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain…
A few pages in Siegel describe how, starting with a fundamental polygon for a compact Riemann surface, one can construct a symplectic basis of its homology. This note retells that construction, specializing to the case where the surface is…
We calculate the cohomology of $\mathfrak{sl}_3(k)$ over an algebraically closed field $k$ of characteristic $p>3$ with coefficients in simple modules and Weyl modules. We also give descriptions of the corresponding cohomology of…
We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution…
This is an abstract for my talk at the 68th Geometry Symposium on August 31, 2021. It is based on my joint work in progress with Dinakar Muthiah: a conjectural characterization of the equivariant costalk of the intersection cohomology…
The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise…
We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some…
In this paper, we study combinatorics of congruence subgroups of the modular group. More precisely, we consider the matrix equation that naturally arises in the theory of Coxeter friezes and investigate its irreducible solutions. We give…
We give the geometric version of a construction of Colmez-Niziol which establishes a comparison theorem between arithmetic p-adic nearby cycles and syntomic sheaves. The local construction of the period isomorphism uses…
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…
Consider the middle perversity intersection cohomology groups of various compactifications of a Hermitian locally symmetric space. Rapoport and independently Goresky and MacPherson have conjectured that these groups coincide for the…
We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple Hessenberg variety becomes a module of a symmetric group…