The Crystals Associated to Barsotti-Tate Groups: With Applications to Abelian Schemes |
Contents
Conventions | 10 |
The Relation between BarsottiTate and Formal | 23 |
Divided Powers Exponentials and Crystals | 77 |
Copyright | |
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The Crystals Associated to Barsotti-Tate Groups: With Applications to ... William Messing Limited preview - 2006 |
Common terms and phrases
abelian scheme abelian variety affine open affine scheme algebra assume augmentation ideal B. T. group b₁ Barsotti Barsotti-Tate group base change bi-algebra bijective canonical lifting Cartier dual co-algebra commutative diagram compatible condition Corollary corresponding Cospec crystals defined definition denote direct limit element epimorphism equivalence of categories étale exact sequence exponential faithfully flat fiber finite and locally finite and locally-free finite locally-free finite presentation finite type formal Lie group formally smooth functor G₂ give given group G group scheme hence Hom G homomorphism hypothesis implies induces Inf G isomorphism kernel Lemma Let G Lie E(G Lie F Lie G Lie H lim G[n linear local ring locally free locally nilpotent morphism nilpotent divided powers notation obtain obvious p-divisible p-torsion phism proposition prove radiciel Remark restriction ring S-group S-scheme satisfies sheaf sheaves Spec surjective Tate group theorem topology unique