Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Cong Xue
Email des responsables : alexis.bouthier@imj-prg.fr, cong.xue@imj-prg.fr
Salle :
Adresse :

Orateur(s) Brian SMITHLING - Max Planck Institut für Mathematik,
Titre Local models for even orthogonal groups
Horaire14:00 à 15:00
RésumeLocal models are schemes, defined in terms of linear algebra, that were introduced by Rapoport and Zink to study the étale-local structure around points in the special fiber of integral models of certain PEL Shimura varieties over $p$-adic fields. A basic requirement for the local models is that they be flat. When the group defining the Shimura variety is split $GO_{2n}$, Genestier observed that the naive definition of the local model does not yield a flat scheme. In a recent preprint, Pappas and Rapoport introduced a new condition to the moduli problem defining the local model, the so-called spin condition, and conjectured that the ``spin'' local models are flat. I will report on some work towards obtaining a better understanding of the spin condition for these schemes.