概形上的刚性对偶复形
代数几何
2020-06-08 v4
摘要
在本文中，我们提出一种处理概形上 Grothendieck 对偶的新方法。我们的方法基于 Van den Bergh 在非交换代数几何背景下引入的刚性对偶复形思想。我们获得了 Grothendieck 对偶的大部分重要性质，同时避免了冗长而困难的相容性验证。我们的结果适用于正则 noether 有限维基环上的有限型概形，因此适用于算术几何。
引用
@article{arxiv.math/0405570,
title = {Rigid Dualizing Complexes on Schemes},
author = {Amnon Yekutieli and James J. Zhang},
journal= {arXiv preprint arXiv:math/0405570},
year = {2020}
}
备注
This preprint is withdrawn because it is sketchy, and the proofs in it are far from complete. The authors are presently working on an improved version of this material (both correct and enhanced). Until then the interested reader can look up: (1) Section 13.5 of the book "Derived Catgeories", Cambridge U. Press 2019, prepublication version arXiv:1610.09640v4. (2) The lecture notes "Residues and Duality for Schemes and Stacks" at https://www.math.bgu.ac.il/~amyekut/lectures/resid-stacks/abstract.html