Automorphism Groups of Quasi-galois Closed Arithmetic Schemes

Details Automorphism Groups of Quasi-galois Closed Arithmetic Schemes Automorphism Groups of Quasi-galois Closed Arithmetic Schemes

2009-07-05

arxiv.org/abs/0907.0842v2

Mathematics

Algebraic Geometry

Sharpened the main result; Added three references; Removed minor typos. 29 pages

Scientific paper

Assume that $X$ and $Y$ are arithmetic schemes, i.e., integral schemes of finite types over $Spec(\mathbb{Z})$. Then $X$ is said to be quasi-galois closed over $Y$ if $X$ has a unique conjugate over $Y$ in some certain algebraically closed field, where the conjugate of $X$ over $Y$ is defined in an evident manner. Now suppose that $\phi:X\to Y$ is a surjective morphism of finite type such that $X$ is quasi-galois closed over $Y$. In this paper the main theorem says that the function field $ k(X)$ is canonically a Galois extension of $k(Y)$ and the automorphism group ${Aut}(X/Y)$ is isomorphic to the Galois group $Gal(k(X)/k(Y))$; in particular, $\phi$ must be affine. Moreover, let $\dim X=\dim Y$. Then $X$ is a pseudo-galois cover of $Y$ in the sense of Suslin-Voevodsky.

Affiliated with

Also associated with

No associations

Rating

Automorphism Groups of Quasi-galois Closed Arithmetic 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 Automorphism Groups of Quasi-galois Closed Arithmetic Schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Automorphism Groups of Quasi-galois Closed Arithmetic Schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-187416