Equivariant Brauer and Picard groups and a Chase–Harrison–Rosenberg exact sequence

Equivariant Brauer groups and cohomology ✩

In this paper we present a cohomological description of the equivariant Brauer group relative to a Galois finite extension of fields endowed with the action of a group of operators. This description is a natural generalization of the classic Brauer–Hasse–Noether’s theorem, and it is established by means of a three-term exact sequence linking the relative equivariant Brauer group, the 2nd cohomo...

The Equivariant Brauer Groups of Principal Bundles

Hopf-galois Extensions and an Exact Sequence for H-picard Groups

1 → H(H,Z(A)) g1 → Pic(A) g2 → Pic(A) g3 → H(H,Z(A)). Here H∗(H,Z(AcoH)) are the Sweedler cohomology groups (with respect to the Miyashita-Ulbrich action of H on Z(AcoH)), Pic(AcoH)H is the group of H-invariant elements of Pic(AcoH) and Pic(A) is the group of isomorphism classes of invertible relative Hopf bimodules. We shall give later more details about these notations. Moreover, g1 and g2 ar...

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

The Equivariant Brauer Group of a Group

We consider the Brauer group BM(k, G) of a group G (finite or infinite) over a commutative ring k with identity. A split exact sequence 1 −→ Br′(k) −→ BM′(k, G) −→ Gal(k, G) −→ 1 is obtained. This generalizes the Fröhlich-Wall exact sequence ([7, 8])from the case of a field to the case of a commutative ring, and generalizes the PiccoPlatzeck exact sequence ([13]) from the finite case of G to th...