Related papers: Hilbert 90 for Galois cohomology

We prove that two arithmetically significant extensions of a field F coincide if and only if the Witt ring WF is a group ring Z/n[G]. Furthermore, working modulo squares with Galois groups which are 2-groups, we establish a theorem…

The paper is concerned with the following version of Hilbert's irreducibility theorem: if $\pi: X \to Y$ is a Galois $G$-covering of varieties over a number field $k$ and $H \subset G$ is a subgroup, then for all sufficiently large and…

This paper aims to prove a version of the Hilbert's Theorem 90 for a field with non-trivial Kaplansky radical and the Galois group of its maximal $2$-extension as a finitely generated elementary type pro-2 group.

For an arbitrary field p-torsion and cotorsion of the Milnor groups K_n(F) and K_n^{t}(F)=K_n(F)/\cap_{l\ge1} lK_n(F) are discussed. The work contains further discussions of an analogue of Satz 90 for K_n(F) and K_n^{t}(F) and computation…

We prove the "divisible case" of the Milnor-Bloch-Kato conjecture (which is the first step of Voevodsky's proof of this conjecture for arbitrary prime l) in a rather clear and elementary way. Assuming this conjecture, we construct a 6-term…

The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to…

We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations, and their relationship with the Bloch-Kato conjecture proved by Rost and Voevodsky with Weibel's patch. Our main…

We introduce a condition for Hopf-Galois extensions that generalizes the notion of Kummer Galois extension. Namely, an $H$-Galois extension $L/K$ is $H$-Kummer if $L$ can be generated by adjoining to $K$ a finite set $S$ of eigenvectors for…

The famous Bloch--Kato conjecture implies that for a field $F$ containing a primitive $p$th root of unity, the cohomology ring of the absolute Galois group $G_F$ of $F$ with $\mathbb{F}_p$ coefficients is generated by degree one elements.…

We give a criterion for the cohomological dimension of a field, involving norm maps on Milnor K-theory; this criterion was originally formulated by Kato. The theorem we prove is a generalization of a theorem in Serre's book on Galois…

Let $L/K$ be a finite Galois, totally ramified $p$-extension of complete local fields with perfect residue fields of characteristic $p>0$. In this paper, we give conditions, valid for any Galois $p$-group $G={Gal}(L/K)$ (abelian or not) and…

We show a version of Hilbert 90 that is valid for a large class of algebras many of which are not commutative, distributive or associative. This class contains the nth iteration of the Conway-Smith doubling procedure. We use our version of…

We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps…

Let F be an arbitrary family of subgroups of a group G and let Orb be the associated orbit category. We investigate interpretations of low dimensional F-Bredon cohomology of G in terms of abelian extensions of Orb. Specializing to fixed…

Let p be a prime and F a field containing a primitive pth root of unity. Then for n in N, the cohomological dimension of the maximal pro-p-quotient G of the absolute Galois group of F is <=n if and only if the corestriction maps H^n(H,Fp)…

We define $H$-Galois extensions for $k$-linear categories and a Hopf algebra $H$ and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology, related to this situation. This spectral sequence is…

This work is motivated by the search for an "explicit" proof of the Bloch-Kato conjecture in Galois cohomology, proved by Voevodsky. Our concern here is to lay the foundation for a theory that, we believe, will lead to such a proof- and to…

It it shown that the Bloch-Kato conjecture on the norm residue homomorphism $K^M(F)/l \to H^*(G_F,Z/l)$ follows from its (partially known) low-degree part under the assumption that the Milnor K-theory algebra $K^M(F)/l$ modulo $l$ is…

Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group G_F of F. Using the Bloch-Kato Conjecture we determine the structure of the cohomology group H^n(U,Fp)…

We study the question of the surjectivity of the Galois correspondence from subHopf algebras to subfields given by the Fundamental Theorem of Galois Theory for abelian Hopf Galois structures on a Galois extension of fields with Galois group…