Compactification of Level Maps of Moduli Spaces of Drinfeld Shtukas
Abstract
We define Drinfeld level structures for Drinfeld shtukas of any rank and show that their moduli spaces are regular and admit finite flat level maps. In particular, the moduli spaces of Drinfeld shtukas with Drinfeld $\Gamma_0(\mathfrak{p}^n)$level structures provide a good integral model and relative compactification of the moduli space of shtukas with naive $\Gamma_0(\mathfrak{p}^n)$level defined using shtukas for dilated group schemes.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.09371
 arXiv:
 arXiv:2205.09371
 Bibcode:
 2022arXiv220509371B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory
 EPrint:
 32 pages, final version, to appear in Journal of Algebra