Related papers: Connecting homomorphisms associated to Tate sequen…

The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…

Let A be an abelian variety over C such that the semisimple part of the Hodge group of A is a product of copies of SU(p,1) for some p>1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology of A is…

In Remarks on Galois Cohomology and Definability [2], Pillay introduced definable Galois cohomology, a model-theoretic generalization of Galois cohomology. Let $M$ be an atomic and strongly $\omega$-homogeneous structure over a set of…

A fundamental theorem of Katz \cite{Katz87} determines the differential Galois groups of rank $n$ connections on algebraic curves with slope $r/n$ at a singularity, where $\gcd(r,n)=1$. We extend this result to $G$-connections, where $G$ is…

The recently introduced Galois symmetries of RCFT are generalized, for the WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrix S,…

Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein rings. This paper improves the theory further by giving a new…

Let G be a connected, compact, semisimple algebraic group over the field of real numbers R. Using Kac diagrams, we describe combinatorially the first Galois cohomology sets H^1(R,H) for all inner forms H of G. As examples, we compute…

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…

Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In…

In this article, we first briefly introduce the history of the Weil-\'etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the Weil-etale cohomology…

We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups and to global Galois extensions. We describe parts of the general…

By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…

Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor $N$…

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…

One of the key points in Galois theory via field extensions is to build up a correspondence between subfields of a field and subgroups of its automorphism group, so as to study fields via methods of groups. As an analogue of the Galois…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

A Galois connection between clones and relational clones on a fixed finite domain is one of the cornerstones of the so-called algebraic approach to the computational complexity of non-uniform Constraint Satisfaction Problems (CSPs). Cohen…

In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we will show that those combined extensions can be made if we…

Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$. However, we also construct $A$-modules which…

We study transchromatic phenomena for the Tate construction of Real oriented cohomology theories. First, we show that after suitable completion, the Tate construction with respect to a trivial $\mathbb{Z}/2$-action on height $n$ Real…