Moduli spaces of 𝑝-divisible groups

Abstract

We study the global structure of moduli spaces of quasi-isogenies of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -divisible groups are simple, we compute the cohomology of the moduli space. As an application we determine which moduli spaces are smooth.