Related papers: Period-like polynomials for $L$-series associated …

We prove a version of Ihara's Lemma for degree q=1,2 cuspidal cohomology of the symmetric space attached to automorphic forms of arbitrary weight (k\geq 2) over an imaginary quadratic field with torsion (prime power) coefficients. This…

In a paper published in 1959, Shimura presented an elegant calculation of the critical values of L-functions attached to elliptic modular forms using the first cohomology group. We will show that a similar calculation is possible for…

We compute tables of paramodular forms of degree two and cohomological weight via a correspondence with orthogonal modular forms on quinary lattices.

We extend to positive real weights Haberland's formula giving a cohomological description of the Petersson scalar product of modular cusp forms of positive even weight. This relation is based on the cup product of an Eichler cocycle and a…

Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper-half plane, has…

We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…

We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group $\Gamma<\text{Isom}(\mathbb{H}^{n+1})$, each full rank cusp corresponds to a cohomology class in…

In this paper we establish a connection between the cohomology of a modular Lie algebra and its p-envelopes. We also compute the cohomology of Zassenhaus algebras and their minimal p-envelopes with coefficients in generalized baby Verma…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…

We prove that the morphisms from a minimal Sullivan algebra $\Lambda V$ to $A_{PL}(|\Lambda V|)$, the algebra of polynomial differential forms on its realization, can be quasi-isomorphic if and only if the cohomology $H(\Lambda V)$ is of…

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…

A Koszul duality-type correspondence between coderived categories of conilpotent differential graded Lie coalgebras and their Chevalley-Eilenberg differential graded algebras is established. This gives an interpretation of Lie coalgebra…

We introduce the notion of \textit{relative $L^p$-cohomology} as a quasi-isometry invariant defined for Gromov-hyperbolic spaces, and apply it to the problem of quasi-isometry classification of Heintze groups. More precisely, we explicitly…

We consider the period polynomials $r_f(z)$ associated with cusp forms $f$ of weight $k$ on all of $\mathrm{SL}_2\left( \mathbb{Z} \right)$, which are generating functions for the critical $L$-values of the modular $L$-function associated…

We propose to associate to a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequence in terms of the Mellin…

Notable results on the special values of $L$-functions of Siegel modular forms were obtained by J. Sturm in the case when the degree $n$ is even and the weight $k$ is an integer. In this paper we extend this method to half-integer weights…

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to…

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial)…