CM-lifts for Isogeny Classes of Shimura F-crystals over Finite Fields

Abstract

We extend to large contexts pertaining to Shimura varieties of Hodge type a result of Zink on the existence of lifts to characteristic 0 of suitable representatives of certain isogeny classes of abelian varieties endowed with Frobenius and other endomorphisms over $\dbF_{p^q}$, whose $p$-divisible groups in mixed characteristic $(0,p)$ are with complex multiplication.

Shorter version 62 pages

References in corpus (5)

• Some cases of the Mumford--Tate conjecture and Shimura varieties
• Manin problems for Shimura varieties of Hodge type
• Projective integral models of Shimura varieties of Hodge type with compact factors
• On two theorems for flat, affine group schemes over a discrete valuation ring
• Generalized Serre--Tate Ordinary Theory

Cited by in corpus (2)

• The Tate conjecture over finite fields (AIM talk)
• Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport