Related papers: L-modules and micro-support

Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in…

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…

Let X be the locally symmetric space associated to a reductive $\mathbb Q$-group G and an arithmetic subgroup $\Gamma$. An L-module M is a combinatorial model of a constructible complex of sheaves on $\widehat X$, the reductive Borel-Serre…

This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the…

The $L^2$-cohomology of a locally symmetric variety is known to have the topological interpretation as the intersection homology of its Baily-Borel Satake compactification. In this article, we observe that even without the Hermitian…

In this manuscript we consider the extent to which an irreducible representation for a reductive Lie group can be realized as the sheaf cohomolgy of an equivariant holomorphic line bundle defined on an open invariant submanifold of a…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

Let $X$ be a projective manifold, and $D$ be a normal crossing divisor of $X$. By Jost-Zuo's theorem that if we have a reductive representation $\rho$ of the fundamental group $\pi_{1}(X^{*})$ with unipotent local monodromy, where…

A cohomological support, Supp_A(M), is defined for finitely generated modules M over an left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the…

By using our previous results on L\^e modules and an upper-bound on the betti numbers which we proved with L\^e, we investigate the cohomology of Milnor fibers and the internal local systems given by the vanishing cycles of hypersurfaces…

We explore the cohomological structure for the (possibly singular) moduli of $\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divisor of degree >2g-2. We prove a support theorem for the…

Let $L$ be a finite dimensional Lie algebra over a field of characteristic $0$. Then by the original Levi theorem, $L = B \oplus R$ where $R$ is the solvable radical and $B$ is some maximal semisimple subalgebra. We prove that if $L$ is an…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector…

We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma$-support of $L$ coincides with the reduced micro-support…

Let $A$ be an associative ring and $M$ a finitely generated projective $A$-module. We introduce a category $\operatorname{RBS}(M)$ and prove several theorems which show that its geometric realisation functions as a well-behaved unstable…

Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $\rho: \pi_1(S)\to Sl(n, \mathbb{C})$ be a semisimple linear representation of $\pi_1(S)$ which is unipotent near…

We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…

Let $G$ be a real linear reductive group and let $H$ be a unimodular, locally algebraic subgroup. Let $\operatorname{supp} L^2(G/H)$ be the set of irreducible unitary representations of $G$ contributing to the decomposition of $L^2(G/H)$,…

We prove an analogue for Hodge modules of Pink's theorem on the degeneration of l-adic sheaves (Math. Ann. 292). Let j be the open immersion of a Shimura variety M into its Baily-Borel compactification. Its boundary has a natural…