Related papers: A Separated Cohomologically Complete Module is Com…
In [5], the notion of polynomial cocycles is used to give an expression for the second cohomology of T-groups with coefficients in a torsion-free nilpotent module. We make this expression concrete in the case of a T-group G of nilpotency…
It is proved that any polynomial vector field in two complex variables which is complete on a non-algebraic trajectory is complete.
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…
We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate…
We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and…
We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class CogenM is always a covering class whenever M is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given. As…
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The…
We describe cohomological conditions that are necessary and sufficient for the existence of balanced dualizing dg-modules, generalizing a theorem of Van den Bergh for balanced dualizing complexes over graded algebras. As a consequence, we…
We prove two polynomial identities which are particular cases of a conjecture arising in the theory of L-functions of twisted Carlitz modules. This conjecture is stated in earlier papers of the second author.
In this article, we present actions by central elements on Hochschild cohomology groups with arbitrary bimodule coefficients, as well as an interpretation of these actions in terms of exact sequences. Since our construction utilises the…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein) projective dimension with respect to a semidualizing module. We also verify special cases of a question of…
If $R$ is a commutative unital ring and $M$ is a unital $R$-module, then each element of $\operatorname{End}_R(M)$ determines a left $\operatorname{End}_{R}(M)[X]$-module structure on $\operatorname{End}_{R}(M)$, where…
A Lefschetz module is a module over a graded algebra $A$ that satisfies analogues of Poincar\'{e} duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to an open convex cone $\mathscr{K}$ in the degree one…
By analogy with the classical (Chasles-Schubert-Semple-Tyrell) spaces of complete quadrics and complete collineations, we introduce the variety of complete complexes. Its points can be seen as equivalence classes of spectral sequences of a…
We establish an explicit quasi-isomophism of complexes, which is homogeneous in graded situation, from a given Cech complex of modules of generalized fractions.
We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$…
We prove that the monodromy of an irreducible cohomologically complex rigid local system with finite determinant and quasi-unipotent local monodromies at infinity on a smooth quasiprojective complex variety $X$ is integral. This answers…
This is a largely expository paper, providing a self-contained account on the results of [Sch-Si1, Sch-Si2], in the cases denoted there 2Q and 2M. These papers of Sch\"afke and Singer supplied new proofs to the main theorems of [Bez-Bou,…
In this paper, we introduce and study the notions of uniformly $S$-finitely presented modules and uniformly $S$-coherent rings (modules) which are "uniform" versions of ($c$-)$S$-finitely presented modules and ($c$-)$S$-coherent rings…