Related papers: Denominators of Eisenstein cohomology classes for …

A general conjecture of Harder relates the denominator of the Eisenstein cohomology of certain locally symmetric spaces to special values of $L$-functions. In this paper we consider the locally symmetric space…

We study the arithmetic of degree $N-1$ Eisenstein cohomology classes for locally symmetric spaces associated to $\mathrm{GL}_N$ over an imaginary quadratic field $k$. Under natural conditions we evaluate these classes on $(N-1)$-cycles…

For certain algebraic Hecke characters chi of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL_2/F. By finding congruences between Eisenstein cohomology…

In this article, Eisenstein cohomology of the arithmetic group $G_2(\mathbb{Z})$ with coefficients in any finite dimensional highest weight irreducible representation has been determined. We accomplish this by studying the cohomology of the…

In this article, several cohomology spaces associated to the arithmetic groups $\mathrm{SL}_3(\mathbb{Z})$ and $\mathrm{GL}_3(\mathbb{Z})$ with coefficients in any highest weight representation $\mathcal{M}_\lambda$ have been computed,…

In this paper we compute the cohomology groups of GL(4,Z) with coefficients in symmetric powers of the standard representation twisted by the determinant. This problem arises in Goncharov's approach to the study of motivic multiple zeta…

This is an expository article that concerns the various related notions of algebraic idele class characters, the Groessencharaktere of Hecke, and cohomological automorphic representations of GL(1), all under the general title of algebraic…

Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be the congruence subgroup of level n consisting of matrices…

We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes restricting…

We construct Eisenstein cocycles for arithmetic subgroups of GL_2 of imaginary quadratic fields valued in second K-groups of products of two CM elliptic curves. We use these to construct maps from the first homology groups of Bianchi spaces…

We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational…

We give a new, purely topological construction of Eisenstein cohomology classes for Hilbert-Blumenthal varieties using the polylogarithm for families of topological tori and a decomposition with respect to the units in the center of $GL_2$.…

Let $F$ be a CM field, let $p$ be a prime number. The goal of this paper is to show, under mild conditions, that the modulo $p$ cohomology of the locally symmetric spaces $X$ for $GL_2(F)$ with level prime to $p$ is concentrated in degrees…

For a finite abelian 2-group $G$, we study the frequency with which quadratic imaginary number fields $K$ have 2-part of their class group $K$ isomorphic to $G$. A philosophy enunciated by Gerth extends the Cohen-Lenstra heuristics for…

M. Goresky, G. Harder, and R. MacPherson defined weighted cohomologies of arithmetic groups \Gamma in a real group G, with coefficients in certain local systems, associated to arbitrary upper and lower weight profiles. The author shows,…

We establish results on the rationality of ratios of successive critical values of Langlands-Shahidi $L$-functions, as they appear in the constant term of the Eisenstein series associated with the exceptional group of type $G_2$ over a…

We study the local Hecke algebra $\mathcal{H}_{G}(K)$ for $G = \mathrm{GL}_n$ and $K$ a non-archimedean local field of characteristic zero. We show that for $G = \mathrm{GL}_2$ and any two such fields $K$ and $L$, there is a Morita…

Let $\rho$ be a two-dimensional even Galois representation which is induced from a character $\chi$ of odd order of the absolute Galois group of a real quadratic field. After imposing some additional conditions on $\chi$, we attach $\rho$…

We show that for an arbitrary totally complex number field $L$ the (regularized) critical $L$-values of algebraic Hecke characters of $L$ divided by certain periods are algebraic integers. This relies on a new construction of an equivariant…

Rationality results are proved for the ratios of critical values of Rankin-Selberg L-functions of GL(n) x GL(n') over a totally imaginary field F, by studying rank-one Eisenstein cohomology for the group GL(N)/F, where N = n+n',…