Related papers: Twisted Cyclic Cohomology and Modular Fredholm Mod…
Motivated by classical facts concerning closed manifolds, we introduce a strong finiteness property in K-homology. We say that a C*-algebra has uniformly summable K-homology if all its K-homology classes can be represented by Fredholm…
We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a…
Let G be a complex reductive group and X a projective spherical G-variety. Moreover, assume that the subalgebra A of the cohomology ring H^*(X, R) generated by the Chern classes of line bundles has Poincare duality. We give a description of…
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…
In this paper, we construct Chern classes from the relative $K$-theory of modulus pairs to the relative motivic cohomology defined by Binda-Saito. An application to relative motivic cohomology of henselian dvr is given.
We study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system $\mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver to twisted…
Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is finitely…
Let $W$ be a finite Weyl group and $\sg$ be a non-trivial graph automorphism of $W$. We show a remarkable relation between the $\sg$-twisted involution module for $W$ and the Frobenius--Schur indicators of the unipotent characters of a…
Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first…
The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of…
In this paper we introduce and develop the theory of FI-modules. We apply this theory to obtain new theorems about: - the cohomology of the configuration space of n distinct ordered points on an arbitrary (connected, oriented) manifold -…
We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for the coaction of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras,…
We prove the multiplicative property of localized Chern characters. As a direct consequence, a localized Chern character gives rise to a ring homomorphism from the K-group of periodic complexes to the bivariant Chow cohomology group. As an…
This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…
For any space X with the homotopy type of simply-connected, finite-type CW-complex, we construct an associative cochain algebra fls(X) whose cohomology algebra is isomorphic to that of LX, the free loop space on X. For certain X, we define…
We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a…
In this short note we define a new cohomology for a Lie algebroid $\mathcal{A}$, that we call the \emph{twisted cohomology} of $\mathcal{A}$ by an odd cocycle $\theta$ in the Lie algebroid cohomology of $\mathcal{A}$. We proof that this…
Following Bloch-Esnault-Kerz and Green-Griffiths' recent works on deformation of algebraic cycle classes, we use Chern character from K-theory to negative cyclic homology to show how to eliminate obstructions to deforming cycles.
In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and…
Spencer cohomology theory studies the cohomology of chain complexes of modules over the ring of differential operators $\mathscr{D}$ of a smooth analytic space. In this paper we give a generalisation of Spencer cohomology suitable for…