Related papers: Cohomology of profinite groups of bounded rank

As a sequel of Part I, we consider a filtration of Hodge cohomology groups indexed by divisors "at infinity", and prove that they are represented in the category of motives with modulus. In particular, we obtain a realisation functor of the…

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.

We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.

We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…

For every imprimitive complex reflection group of rank 2, we construct a semi-orthogonal decomposition of the derived category of the associated global quotient stack which categorifies the usual decomposition of the orbifold cohomology…

We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…

We give a characterization of finite pointed tensor categories obtained as de-equivariantizations of finite-dimensional pointed Hopf algebras over abelian groups only in terms of the (cohomology class of the) associator of the pointed part.…

We introduce a criterion on the presentation of finitely presented pro-$p$ groups which allows us to compute their cohomology groups and infer quotients of mild groups of cohomological dimension strictly larger than two, from (non-free)…

On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology…

We introduce a refinement of bounded cohomology and prove that the suitable comparison homomorphisms vanish for an amenable group. We investigate in this context Thompson's group F and provide further evidence towards its amenability. We…

The goal of this paper is to present results which are consistent with conjectures about the Leibniz (co)homology for discrete groups stated by J. L. Loday. We show that rack cohomology has properties very close to the properties expected…

The article deals with profinite groups in which the centralizers are abelian (CA-groups), that is, with profinite commutativity-transitive groups. It is shown that such groups are virtually pronilpotent. More precisely, let G be a…

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.

In this short note, we present a persistence module approach to directed cohomology, dual to the directed homology introduced by the author in a previous article. We lay out the first properties of directed cohomology and in particular of…

We use Jiang--Pareschi's cohomological rank functions and techniques developed by Caucci and Ito to study syzygies of projective bundles on abelian varieties. Consequently, we generalize and refine Chiantipalli's results regarding property…

We develop an algebro-analytic framework for the systematic study of the continuous bounded cohomology of Lie groups in large degree. As an application, we examine the continuous bounded cohomology of PSL(2,R) with trivial real coefficients…

We introduce the category of finite Chow-Witt correspondences over a perfect field k of characteristic not 2. We then use them to define bigraded generalized motivic cohomology groups of a smooth scheme over k and begin the study of their…

We give an interpretation of the Brauer group of a purely inseparable extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted Lie-Rinehart…