正特征下通用曲线的有理点
代数几何
2016-01-25 v2
摘要
对于具有函数域 的 上光滑曲线的模栈 ，我们证明若 ，则 上通用曲线的唯一 -有理点是其 个重言点。此外，我们证明若 且 ，则 Grothendieck 截面猜想对 上的通用曲线成立。这是将 Hain 在特征 0 下的工作推广到正特征。
引用
@article{arxiv.1410.3020,
title = {Rational points of universal curves in positive characteristics},
author = {Tatsunari Watanabe},
journal= {arXiv preprint arXiv:1410.3020},
year = {2016}
}
备注
31 pages. Significantly shortened. Proposition 4.3 from the 1st version had a mistake and is replaced with a weaker proposition. This article draws heavily from arXiv:1001.5008 "Rational points of universal curve." by Richard Hain and is an extension from char. zero to positive characteristic