The Brauer group and the Brauer-Manin set of products of varieties

Details The Brauer group and the Brauer-Manin set of products of varieties The Brauer group and the Brauer-Manin set of products of varieties

2011-12-14

arxiv.org/abs/1112.3089v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

Let $X$ and $Y$ be smooth and projective varieties over a field $k$ finitely generated over $\mathbb Q$, and let $\ov X$ and $\ov Y$ be the varieties over an algebraic closure of $k$ obtained from $X$ and $Y$, respectively, by extension of the ground field. We show that the Galois invariant subgroup of $\Br(\ov X)\oplus \Br(\ov Y)$ has finite index in the Galois invariant subgroup of $\Br(\ov X\times\ov Y)$. This implies that the cokernel of the natural map $\Br(X)\oplus\Br(Y)\to\Br(X\times Y)$ is finite when $k$ is a number field. In this case we prove that the Brauer-Manin set of the product of varieties is the product of their Brauer-Manin sets.

Affiliated with

Also associated with

No associations

Rating

The Brauer group and the Brauer-Manin set of products of varieties 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 The Brauer group and the Brauer-Manin set of products of varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Brauer group and the Brauer-Manin set of products of varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-225284