Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes
| dc.creator | Nakaoka, Hiroyuki | |
| dc.date | 2008-11-15 | |
| dc.date.accessioned | 2026-07-07T10:18:42Z | |
| dc.date.available | 2026-07-07T10:18:42Z | |
| dc.description | Past studies of the Brauer group of a scheme tells us the importance of the interrelationship among Brauer groups of its finite étale 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 étale coverings. For any finite étale 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. | |
| dc.identifier | https://arxiv.org/abs/0811.2505 | |
| dc.identifier | http://arxiv.org/abs/0811.2505 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174275 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Mackey-functor structure on the Brauer groups of a finite Galois covering of schemes | |
| dc.type | text |