Related papers: On finitely summable Fredholm modules from Smale s…

We show that the spectral radius for the action of a self map $f$ of a smooth projective variety (over an arbitrary base field) on its $\ell$-adic cohomology is achieved on the $f^*$-stable sub-algebra generated by any ample class. This…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean field. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group. The…

To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new…

We consider pairs of maps from a discrete group to the unitary group. The deficiencies of these maps from being homomorphisms may be great, but if they are close to each other then we call such pairs balanced. We show that balanced pairs…

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a compact…

We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases…

Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate…

We define classes of pseudodifferential operators on $G$-bundles with compact base and give a generalized $L^2$ Fredholm theory for invariant operators in these classes in terms of von Neumann's $G$-dimension. We combine this formalism with…

In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let $S$ be a graded ($\pm 1$)-skew polynomial algebra in $n$ variables of degree $1$ and $f =x_1^2 + \cdots +x_n^2…

We introduce tame sc-Fredholm sections and slices of sc-Fredholm sections. A slice is a notion of subpolyfold that is compatible with the sc-Fredholm section and has finite locally constant codimension. We prove that the subspace of a tame…

Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of…

The main result of this paper amounts to a complete evaluation of the integral cohomological structure of the stable mapping class group. In particular it verifies the conjecture of D.Mumford about the rational cohomology of the stable…

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$--semistable principal $H$--bundles over a {\it smooth projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth projective…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

We prove that the singular cohomology with finite coefficients of a finite-dimensional Stein space $S$ is isomorphic to the \'etale cohomology of the Stein algebra $\mathcal{O}(S)$. We deduce that any class in $H^k(S,\mathbb{Z})$ comes from…

An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $\widehat{R}$ its $\mathfrak{m}$-adic completion. We study the problem of determining when a finitely generated $\widehat{R}$-module arises from an $R$-module, i.e., when it is…

In this paper we investigate the arithmetic aspects of the theory of $\mathcal{E}_K^\dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology groups have compatible connections and…

We study Demazure modules which occur in a level $\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie…