Abstract
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.
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Acknowledgements
We would like to thank Wushi Goldring for very useful discussions. This work is a continuation of a joint project with him. We are also grateful to David Helm for helpful advice. Finally, we would like to thank the referee for his remarks and suggestions on a first version of the paper. The author is a JSPS International Research Fellow (Graduate School of Mathematics, Tokyo University).
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