晶体上同调中的变分 Tate 猜想
代数几何
2015-03-26 v2 K理论与同调
摘要
给定特征下的光滑真簇族，以及该族某纤维上的一个圈，我们提出了一个变分 Tate 猜想，该猜想利用的晶体圈类来刻画是否在上同调意义上扩展到整个簇族。这是 Grothendieck 变分 Hodge 猜想在特征下的类比。我们证明了该猜想对除子成立，并对更高余维数的圈证明了该猜想的一个无穷小变体。此结果可用于将有限域上除子的-进 Tate 猜想归约到曲面情形。
引用
@article{arxiv.1408.6783,
title = {A Variational Tate Conjecture in crystalline cohomology},
author = {Matthew Morrow},
journal= {arXiv preprint arXiv:1408.6783},
year = {2015}
}
备注
The former Section 3.3, containing a sketched treatment of line bundles with Q_p-coefficients, has been removed as an error was found. This affects the validity of none of the main results, but necessitates giving a different proof of the application to the Tate Conjecture. Other minor changes