On a Class of 2-Periodic Cohomology Theories.
In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz’s prediction that their -adic...
Let be the ring of integers of a totally real field of degree . We study the reduction of the moduli space of separably polarized abelian -varieties of dimension modulo for a fixed prime . The invariants and related conditions for the objects in the moduli space are discussed. We construct a scheme-theoretic stratification by -types on the Rapoport locus and study the relation with the slope stratification. In particular, we recover the main results of Goren and Oort [J. Alg. Geom.,...