周期映射的 Satake-Baily-Borel 类比
代数几何
2025-04-08 v6
摘要
我们提出了任意周期映射的 Satake-Baily-Borel 紧化与 Borel 扩张定理的一个类比。所提出的类比被构造为周期映射的一个恰当拓扑完备化。我们猜想该构造是射影代数的，并将该猜想归结为某个扩张问题。
引用
@article{arxiv.2010.06720,
title = {Analog of Satake-Baily-Borel for period maps},
author = {Mark Green and Phillip Griffiths and Colleen Robles},
journal= {arXiv preprint arXiv:2010.06720},
year = {2025}
}
备注
This is a major revision. The previous version has been separated into two parts; this is Part 1. The previous version erroneously claimed that certain line bundles $\mathrm{det}(F^p)$ descend to the SBB completion. We thank Ben Bakker for providing a counter-example. We are able to show that the product $\prod_p\,\mathrm{det}(F^p)^{\otimes m_p}$ descends, for suitable choice of $m_p > 0$