Related papers: Explicit Chern Cycles in BGL and KV-theory

Bloch and Esnault defined additive higher Chow groups with modulus (m+1) on the level of zero cycles over a field k, denoted by TH^n(k,n;m), n,m >0. They prove that TH^n(k,n;1) is isomorphic to the group of absolute Kaehler differentials of…

In this paper we construct a bivariant Chern character defined on ``families of spectral triples''. Such families should be viewed as a version of unbounded Kasparov bimodules adapted to the category of bornological algebras. The Chern…

We study the modularity of the generating series of special cycles on unitary Shimura varieties over CM-fields of degree $2d$ associated with a Hermitian form in $n+1$ variables whose signature is $(n,1)$ at $e$ real places and $(n+1,0)$ at…

For a discrete group $\Gamma$, we study vector bundles $E_\rho$ on compact subsets of $B\Gamma$ associated to almost representations $\rho:\Gamma \to U(n)$. We compute the first Chern class of $E_\rho$ in terms of $\rho$. When $\rho$ is…

We compute explicit bases for the de Rham cohomology of cyclic covers of the projective line defined over an algebraically closed field of characteristic $p\geq 0$. For both Kummer and Artin-Schreier extensions, we describe precise…

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of…

We obtain a precise relation between the Chern-Schwartz-MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of…

We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups over arbitrary fields and skew fields, with values in the Witt group of hermitian forms. This cocycle has good functorial properties: it is natural under extension…

To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be…

We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincar\'e-dual class of empty loci in the Hodge bundle. We use these relations to obtain a…

We discuss conjectures following from the attractor mechanism in type II string theory about the possible Chern classes of stable holomorphic vector bundles on Calabi-Yau threefolds. In particular, we give sufficient conditions for Chern…

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification…

We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper.…

We begin the study of Khovanov-Lauda-Rouquier type algebras associated to moduli stacks of coherent sheaves on smooth projective curves. We consider the case of $\mathbb{P}^1$ and define, for any pair $(r,d)$ of a rank and a degree, the KLR…

In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In…

The Chern-Dold character of a cohomology theory E is a canonical transformation $E\rightarrow HV$ to ordinary cohomology. A spectrum representing E gives homotopy theoretic cocycles for E, while HV can be represented by singular cocycles.…

We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the…

We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local conformal diffeomorphisms. After defining a K-cycle on the crossed product…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic…