ABSTRACT.
Canonical integral models of Shimura varieties associated to reductive groups that are anisotropic modulo center are expected to be proper. However, the analogous statement is known to fail for moduli stacks of shtukas over global function fields. More specifically, let G be a parahoric group scheme over a smooth proper curve X over a finite field, corresponding to a maximal order of a central division algebra D. Lau established a numerical criterion for the properness of the moduli stack of bounded G-shtukas with legs restricted to the split locus of D. Consequently, there are cases where the moduli stack is not proper over the split locus. Building on the work of Arasteh Rad-Hartl and Bieker, we consider moduli stacks of bounded G-shtukas where the legs are allowed to lie in the ramification locus of D. We extend Lau's result to a setting that includes the ramified case. In particular, we demonstrate that a moduli stack of G-shtukas can be proper when legs are restricted to the split locus, yet fail to be proper when the legs extend over the entire curve. This is joint work with Wansu Kim and Junyeong Park.
CMC Algebra Seminar