Abstract
We give a definition of full level structure on group schemes of the form \(G\times G\), where G is a finite flat commutative group scheme of rank p over a \({\mathbb {Z}}_p\)-scheme S or, more generally, a truncated p-divisible group of height 1. We show that there is no natural notion of full level structure over the stack of all finite flat commutative group schemes.
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Acknowledgements
I would like to thank my advisor George Pappas for his support and encouragement. I thank Preston Wake for very helpful conversations and useful suggestions. I also thank the reviewers for patient reading and helpful suggestions.
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