广义Picard-Vessiot扩张与微分伽罗瓦上同调
代数几何
2017-09-12 v2
摘要
在早先的论文中证明了，如果微分域是代数闭的且在Picard-Vessiot扩张下封闭，则对于K上的线性微分代数群G，K上的每个微分代数主齐性空间都有K有理点（事实上当且仅当）。本文探讨了这是否可以推广到(a)多个导子，(b)一个自同构，如果可以，如何推广。在“广义Picard-Vessiot扩张”（在多导子情形）的自然概念下，我们给出一个反例。在单自同构情形我们也有一个反例。我们还提出并证明了多导子情形的一些肯定命题。
引用
@article{arxiv.1702.01969,
title = {Generalized Picard-Vessiot extensions and differential Galois cohomology},
author = {Zoe Chatzidakis and Anand Pillay},
journal= {arXiv preprint arXiv:1702.01969},
year = {2017}
}
备注
The new version is the one accepted by Annales Math. Toulouse, and makes some clarifications and additions suggested by the referees, including reference to a recent related paper by Minchenko and Ovchinnikov