On degenerations of D -shtukas

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

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Bibliographic Details
Published in:Duke mathematical journal 2007-11, Vol.140 (2), p.351-389, Article 351
Main Author: Lau, Eike
Format: Article
Language:English
Subjects:
11F46
11G18
Arithmetic theory of algebraic function fields [See also 14-XX]
Drinfel'd modules
etc. [See also 14L05]
higher-dimensional motives
Modular and Shimura varieties [See also 11F41
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Summary:Let F be a global field of positive characteristic, and let D be a maximal order in a central division algebra over F . We give a precise properness criterion for moduli spaces of D -shtukas with general modifications, which includes the statement that for some division algebras, the space of ordinary D -shtukas is not proper. The proof is based on a result on the smoothness of a suitable stack of complete homomorphisms of D -modules of rank 1
ISSN:0012-7094
1547-7398
DOI:10.1215/S0012-7094-07-14025-0