Related papers: Characters of Cycles, Equivariant Characteristic C…
We show that the bivariant Chern character in entire cyclic cohomology constructed in a previous paper in terms of superconnections and heat kernel regularization, retracts on periodic cocycles under some finite summability conditions. The…
In this report we give an intrinsic treatment of the results we developed in a previous work connecting the differential calculi on Hopf algebras to the Drinfeld double. In the first place we recover that bicovariant bimodules are in one to…
We study relative and logarithmic characteristic cycles associated to holonomic $\mathscr D$-modules. As applications, we obtain: (1) an alternative proof of Ginsburg's log characteristic cycle formula for lattices of regular holonomic…
Based on the ideas of Cuntz and Quillen, we give a simple construction of cyclic homology of unital algebras in terms of the noncommutative de Rham complex and a certain differential similar to the equivariant de Rham differential. We…
A cyclic cohomology theory adapted to Hopf algebras has been introduced recently by Connes and Moscovici. In this paper, we consider this object in the homological framework, in the spirit of Loday-Quillen and Karoubi's work on the cyclic…
We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra {\Omega} and construct its Chern character as a cocycle on the entire cyclic complex of {\Omega}, extending the construction of Jaffe,…
This note discusses the cyclic cohomology of a left Hopf algebroid ($\times_A$-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and…
We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra,…
Associated to a differential character is an integral cohomology class, referred to as the characteristic class, and a closed differential form, referred to as the curvature. The characteristic class and curvature are equal in de Rham…
We prove a moving lemma for the additive and ordinary higher Chow groups of relative $0$-cycles of regular semi-local $k$-schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be…
A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…
We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients…
We construct a triangulated category of cyclotomic complexes, a homological counterpart of cyclotomic spectra of Bokstedt and Madsen. We also construct a version of the Topological Cyclic Homology functor TC for cyclotomic complexes, and an…
For d > 1, we consider the Veronese map of degree d on a complex vector space W , Ver_d : W -> Sym^d W , w -> w^d , and denote its image by Z. We describe the characters of the simple GL(W)-equivariant holonomic D-modules supported on Z. In…
Based on the recent progress in the irregular Riemann-Hilbert correspondence for holonomic D-modules, we show that the characteristic cycles of some standard irregular holonomic D-modules can be expressed as in the classical theorem of…
We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…
In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…
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…
We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with…
I present a generalized notion of obstruction in \v{C}ech cohomology on semi-modules, which allows one to characterize non-disturbing contextual behaviors with any semi-field. This framework generalizes the usual \v{C}ech cohomology used in…