Related papers: Non-Archimedean analytic cyclic homology

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are…

Let $A$ be a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the homological and internal degrees of cochain complexes of graded $A$-modules, providing weighted versions of…

We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…

For a big class of smooth dagger spaces --- dagger spaces are 'rigid spaces with overconvergent structure sheaf' --- we prove finite dimensionality of de Rham cohomology. This is enough to obtain finiteness of Berthelot's rigid cohomology…

We prove that continuous Hochschild and cyclic homology satisfy excision for extensions of nuclear H-unital Frechet algebras and use this to compute them for the algebra of Whitney functions on an arbitrary closed subset of a smooth…

In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H. We show that this family is computable by…

Let $\mathfrak{g}$ be a compact, simple Lie algebra of dimension $d$. It is a classical result that the convolution of any $d$ non-trivial, $G$ -invariant, orbital measures is absolutely continuous with respect to Lebesgue measure on…

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on…

In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology…

Let A_r be the minimal resolution of the cyclic quotient singularity C^2/Z_{r+1}. We study the equivariant quantum cohomology ring of the n-fold symmetric product stack [Sym^n(A_r)] of A_r. We calculate the operators of quantum…

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as…

We show that the diagonal complex computing the Gerstenhaber-Schack cohomology of a bialgebra (that is, the cohomology theory governing bialgebra deformations) can be given the structure of an operad with multiplication if the bialgebra is…

Let R be a perfect F_p-algebra, equipped with the trivial norm. Let W(R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate…

We examine the completely isometric automorphisms of a free product of noncommutative disc algebras. It will be established that such an automorphism is given simply by a completely isometric automorphism of each component of the free…

By considering the Bredon analogue of complete cohomology of a group, we show that every group in the class $\LHFF$ of type Bredon-$\FP_\infty$ admits a finite dimensional model for $\EFG$. We also show that abelian-by-infinite cyclic…

We obtain a mixed complex, simpler that the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values…

$HC_*(A \rtimes G)$ is the cyclic homology of the crossed product algebra $A \rtimes G.$ For any $g \epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A \rtimes G).$…

Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…

Let T be a complete discrete valuation ring and $\hat{X}$ a smooth projective curve over $S=\spec(T)$ with closed fibre $X$. Denote by $F$ the function field of $\hat{X}$ and by $\hat{F}$ the completion of $F$ with respect to the discrete…