On degenerations of D-shtukas

摘要

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-module of rank 1.