On degenerations of {\mathcal D} -shtukas

Let F be a global field of positive characteristic, and let {\mathcal D} be a maximal order in a central division algebra over F . We give a precise properness criterion for moduli spaces of {\mathcal D} -shtukas with general modifications, which includes the statement that for some division algebra...

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Published in:Duke mathematical journal 2007, Vol.140 (no. 2), p.351-389
Main Author: Lau, Eike
Format: Article
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Subjects:
11G09
11R58
14G35
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Summary:Let F be a global field of positive characteristic, and let {\mathcal D} be a maximal order in a central division algebra over F . We give a precise properness criterion for moduli spaces of {\mathcal D} -shtukas with general modifications, which includes the statement that for some division algebras, the space of ordinary {\mathcal D} -shtukas is not proper. The proof is based on a result on the smoothness of a suitable stack of complete homomorphisms of {\mathcal D} -modules of rank 1
ISSN:1547-7398
DOI:10.1215/S0012-7094-07-14025-0