Related papers: On Burghelea Conjecture

Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…

As an extension of an author's previous paper, we prove the Gersten-type conjecture for the mod $p$ \'{e}tale motivic cohomology over a local ring of mixed characteristic $(0, p)$. We also prove the $\mathbb{P}^{1}$-homotopy invariance for…

We prove an extension of the Moore-Schmidt theorem on the triviality of the first cohomology class of cocycles for the action of an arbitrary discrete group on an arbitrary measure space and for cocycles with values in an arbitrary compact…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality…

We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…

We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support…

We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these versions of Koszulity hold for all finitely generated maximal…

Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.

We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.

We consider a class of metabelian groups first studied by Baumslag and Stammbach and we show that these groups are consistent with the Bieri-Groves conjecture which relates cohomological finiteness conditions to the Bieri-Neumann-Strebel…

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…

We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group $W$. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit basis of the…

We give a new proof of Bogomolov's instability theorem. Furthermore we prove that it is equivalent to a statement which characterizes when the first cohomology group of a suitable divisor does not vanish.

We give a proof of the Howe duality conjecture in local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic.

Recently, there has been substantial progress on the Alperin weight conjecture. As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwise Alperin weight condition for simple groups of…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal…

Using cohomology of categories with coefficients in natural systems it is proved that a groupoid enrichad category with pseudoproducts is pseudoequivalent to one with strict products.