2-adic integral canonical models and the Tate conjecture in characteristic 2

2015/12/08 by Wansu Kim, Keerthi Madapusi Pera, Kim, Wansu +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1512.02540

arxiv created 2015/12/08 · arxiv updated 2015/12/09

Abstract

We use E. Lau's classification of 2-divisible groups using Dieudonné displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial. We apply this to prove the Tate conjecture for K3 surfaces in characteristic 2.

Cited by

• Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristic
• Recent progress on the Tate conjecture

Related

• 2-adic integral models of some Shimura varieties with parahoric level structure
• Points of integral canonical models of Shimura varieties of preabelian type, p-divisible groups, and applications. First Part
• Integral canonical models for Spin Shimura varieties
• Integral canonical models of exceptional Shimura varieties
• The Tate conjecture for K3 surfaces in odd characteristic