Potentially good reduction loci of Shimura varieties

Reduction of Shimura varieties at parahoric levels

Good reduction of abelian varieties

Introduction to Shimura Varieties with Bad Reduction of Parahoric Type

This survey article is intended to introduce the reader to several important concepts relating to Shimura varieties with parahoric level structure at p. The main tool is the Rapoport-Zink local model [RZ], which plays an important role in several aspects of the theory. We discuss local models attached to general linear and symplectic groups, and we illustrate their relation to Shimura varieties...

A GUIDE TO THE REDUCTION MODULO p OF SHIMURA VARIETIES

This report is based on my lecture at the Langlands conference in Princeton in 1996 and the series of lectures I gave at the semestre Hecke in Paris in 2000. In putting the notes for these lectures in order, it was my original intention to give a survey of the activities in the study of the reduction of Shimura varieties. However, I realized very soon that this task was far beyond my capabiliti...

Potentially Good Reduction of Barsotti-tate Groups

Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K′ of K. We prove that there exists a constant c ≥ 2 which depends on the absolute ramification index e(K′/Qp) and the height of G such that G ...