On the PiatetskiShapiro construction for integral models of Shimura varieties
Abstract
We study the PiatetskiShapiro construction, which takes a totally real field F and a Shimura datum (G,X) and produces a new Shimura datum (H,Y). If F is Galois, then the Galois group Gamma of F acts on (H,Y), and we show that the Gammafixed points of the Shimura varieties for (H,Y) recover the Shimura varieties for (G,X) under some hypotheses. For Shimura varieties of Hodge type with parahoric level, we show that the same is true for the padic integral models constructed by PappasRapoport, if p is unramified in F. We also study the Gammafixed points of the Igusa stacks of Zhang for (H,Y) and prove optimal results.
 Publication:

arXiv eprints
 Pub Date:
 March 2024
 DOI:
 10.48550/arXiv.2403.10653
 arXiv:
 arXiv:2403.10653
 Bibcode:
 2024arXiv240310653V
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11G18;
 14G35
 EPrint:
 63 pages, comments welcome!