Automorphic forms on the stack of G-Zips. (arXiv:1810.05255v1 [math.NT])

We define automorphic vector bundles on the stack of $G$-zips introduced by Moonen-Pink-Wedhorn-Ziegler and study their global sections. In particular, we give a combinatorial condition on the weight for the existence of nonzero mod $p$ automorphic forms on Shimura varieties of Hodge-type. We attach to the highest weight of the representation $V(\lambda)$ a mod $p$ automorphic form and we give a modular interpretation of this form in some cases. 查看全文>>