Related papers: Descent cohomology and corings
We give a description of the Picard group of a reductive group over a number field as an abelianized Galois cohomology group. It gives another approach of a result due to Labesse.
Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or hereditary torsion pairs) in various derived categories of…
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…
In the category of abelian groups, Pareigis constructed a Hopf ring whose comodules are differential graded abelian groups. We show that this Hopf ring can be obtained by combining grading and differential Hopf rings using semidirect…
A pseudo-Galois extension is shown to be a depth two extension. Studying its left bialgebroid, we construct an enveloping Hopf algebroid for the semi-direct product of groups, or more generally involutive Hopf algebras, and their module…
This paper is concerned with the nonabelian cohomology of groups with coefficients in crossed modules. These objects were introduced by Dedecker and studied by Breen, Borovoi, Noohi and many others. In this paper we study several important…
For an arbitrary 5-fold ramified covering between compact Riemann surfaces, every possible Galois closure is determined in terms of the ramification data of the map; namely, the ramification divisor of the covering map. Since the group that…
Let $X$ be a fine and saturated log scheme, and let $G$ be a commutative finite flat group scheme over the underlying scheme of $X$. If $G$-torsors for the fppf topology can be thought of as being unramified objects by nature, then…
We introduce and study a homology theory of crossed modules with coefficients in an abelian crossed module. We discuss the basic properties of these new homology groups and give some applications. We then restrict our attention to the case…
We study cohomologies of a curve with an action of a finite $p$-group over a field of characteristic $p$. Assuming the existence of a certain 'magical element' in the function field of the curve, we compute the equivariant structure of the…
The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
In this article we construct the inverse semigroup of equivalence classes of partial Galois abelian extensions of a commutative ring R with same group G, called the Harrison partial inverse semigroup.
This manuscript is devoted to the study of the concept of a generating subset (a.k.a. Hopf image of a morphism) in the setting of locally compact quantum groups. The aim of this paper is to provide an accurate description of the Hopf image…
The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups $H$. We provide a unified study of the action of both cover Galois group…
We define comodule algebras and Galois extensions for actions of bialgebroids. Using just module conditions we characterize the Frobenius extensions that are Galois as depth two and right balanced extensions. As a corollary, we obtain…
In this article, we determine cocycle deformations and Galois objects of non-commutative and non-cocommutative semisimple Hopf algebras of dimension $16$. We show that these Hopf algebras are pairwise twist inequivalent mainly by…
In this note, we consider function fields of higher-dimensional algebraic varieties defined over non-local fields, and show how the Galois action on the cohomology such function fields can be used to parameterize their divisorial…
We prove the existence of noncrossed product and indecomposable division algebras over the function field of a smooth p-adic curve, especially when the curve does not admit a smooth model over Z_p. Thus we generalize arXiv 0907.0670. To…
Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.