Hilbert's Theorem 90 and algebraic spaces
代数几何
2007-05-23 v1
摘要
In modern form, Hilbert's Theorem 90 tells us that R^1f_*(G_m)=0, where f is the canonical map between the etale site and the Zariski site of a scheme X. I construct examples showing that the corresponding statement for algebraic spaces does not hold. The first example is a nonseparated smooth 1-dimensional bug-eyed cover in Kollar's sense. The second example is a nonnormal proper algebraic space obtained by identifying points on suitable nonprojective smooth proper schemes.
引用
@article{arxiv.math/0110243,
title = {Hilbert's Theorem 90 and algebraic spaces},
author = {Stefan Schroeer},
journal= {arXiv preprint arXiv:math/0110243},
year = {2007}
}
备注
6 pages, to appear in J. Pure Appl. Algebra