Subrings invariant under endomorphisms
代数几何
2007-05-23 v1
摘要
Let S and R be the rings of regular functions on affine algebraic varieties over a field of characteristic 0, R be embedded as a subring in S, and F : S --> S be an endomorphism such that F(R) subset R. Suppose that every ideal of height 1 in R generates a proper ideal in S, and the spectrum of R has no selfintersection points. We show that if F is an automorphism so is F|_R : R --> R. When R and S have the same transcendence degree then the fact that F|_R is an automorphisms implies that F is an automorphism.
引用
@article{arxiv.math/0208078,
title = {Subrings invariant under endomorphisms},
author = {Shulim Kaliman},
journal= {arXiv preprint arXiv:math/0208078},
year = {2007}
}
备注
16 pages