Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes

Details Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes

2008-11-15

arxiv.org/abs/0811.2505v1

Mathematics

Category Theory

Scientific paper

Past studies of the Brauer group of a scheme tells us the importance of the interrelationship among Brauer groups of its finite \'etale coverings. In this paper, we consider these groups simultaneously, and construct an integrated object "Brauer-Mackey functor". We realize this as a {\it cohomological Mackey functor} on the Galois category of finite \'etale coverings. For any finite \'etale covering of schemes, we can associate two homomorphisms for Brauer groups, namely the pull-back and the norm map. These homomorphisms make Brauer groups into a bivariant functor ($=$ Mackey functor) on the Galois category. As a corollary, Restricting to a finite Galois covering of schemes, we obtain a cohomological Mackey functor on its Galois group. This is a generalization of the result for rings by Ford. Moreover, applying Bley and Boltje's theorem, we can derive certain isomorphisms for the Brauer groups of intermediate coverings.

Affiliated with

Also associated with

No associations

Rating

Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-39467