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

Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain…

We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…

Given a smooth and separated K(pi,1) variety X over a field k, we associate a "cycle class" in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute…

We prove a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective $R_1$-scheme over a field along a closed subscheme, in terms of the Chow groups, with and without modulus, of the scheme. This…

The purpose of this work is to give a definition of a topological K-theory for dg-categories over C and to prove that the Chern character map from algebraic K-theory to periodic cyclic homology descends naturally to this new invariant. This…

In this paper, the homotopy groups of Chow variety $C_{p,d}(P^n)$ of effective $p$-cycles of degree $d$ is proved to be stable in the sense that $p$ or $n$ increases. We also obtain a negative answer to a question by Lawson and Michelsohn…

We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of…

We review and simplify A. Beilinson's construction of a basis for the motivic cohomology of a point over a cyclotomic field, then promote the basis elements to higher Chow cycles and evaluate the KLM regulator map on them.

Let [X/G] be a smooth Deligne-Mumford quotient stack. In a previous paper the authors constructed a class of exotic products called inertial products on K(I[X/G]), the Grothendieck group of vector bundles on the inertia stack I[X/G]. In…

Chain complexes of finitely generated free modules over orbit categories provide natural algebraic models for finite G-CW complexes with prescribed isotropy. We prove a p-hypoelementary Dress induction theorem for K-theory over the orbit…

The classical Chern correspondence states that a choice of Hermitian metric on a holomorphic vector bundle determines uniquely a unitary 'Chern connection'. This basic principle in Hermitian geometry, later generalized to the theory of…

Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than…

For a moduli space of Bridgeland-stable objects on a K3 surface, we show that the Chow class of a point is determined by the Chern class of the corresponding object on the surface. This establishes a conjecture of Junliang Shen, Qizheng…

Higher theta series on moduli spaces of Hermitian shtukas were constructed by Feng--Yun--Zhang and conjectured to be modular, parallel to classical conjectures in the Kudla program. In this paper we prove the modularity of higher theta…

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology of compact Lie group C*-algebras, define Chern characters between them and show that the Chern characters in both topological and…

We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall…

Let p be an odd prime. We show that for a simply-connected semisimple complex linear algebraic group, if its integral homology has p-torsion, the Chern classes do not generate the Chow ring of its classifying space.

For an orthogonal modular variety, we construct a complex which is defined in terms of lattices and elliptic modular forms, which resembles the Gersten complex in Milnor K-theory, and which has a morphism to the Gersten complex of the…

An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to…

We define N-theory being some analogue of K-theory on the category of von Neumann algebras such that $K_0(A)\subset N_0(A)$ for any von Neumann algebra A. Moreover, it turns out to be possible to construct the extension of the Chern…