在$G$-${\tt Zip}^{\mathcal Z}$-概型上具有整体截面的自守向量丛
数论
2017-10-09 v3
摘要
我们陈述了一个关于自守向量丛锥的一般猜想，这些丛在具有以下性质的概型上允许非零整体截面：该概型具有到一个连通Hodge型-zips栈的光滑满射；此类概型应包括所有具有超特殊水平的Hodge型Shimura簇。我们对、型群以及-分裂的型群证明了该猜想（这包括所有Hilbert-Blumenthal簇，并应也适用于Siegel模三维簇和Picard模曲面）。给出一个例子表明对于非连通Hodge型的zip数据，我们的猜想可能不成立。
引用
@article{arxiv.1701.00333,
title = {Automorphic vector bundles with global sections on $G$-${\tt Zip}^{\mathcal Z}$-schemes},
author = {Wushi Goldring and Jean-Stefan Koskivirta},
journal= {arXiv preprint arXiv:1701.00333},
year = {2017}
}
备注
We have added proofs of our global sections cone conjecture for groups of type C_2 and F_p-split groups of type A_2. To this end, the technical focus of the paper has shifted from zip strata to strata of zip flags and the flag space. The introduction has been rewritten to stress two sources of motivation: Hodge theory and the theory of Shimura varieties