Smoothness of the truncated display functor

By E. Lau. 2010

49 citations recorded by the source corpus.

We show that to every p-divisible group over a p-adic ring one can associate a display by crystalline Dieudonne theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic stacks. As an application we obtain a new proof of the equivalence between infinitesimal p-divisible groups and nilpotent displays over p-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of p-power order and Dieudonne modules over perfect rings.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e9ce14c70cfa375730521cfd268da96cb4dd498

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In Geometry and Topology

1. Paul Ziegler
2. R. Pink
3. M. Hoff
4. T. Wedhorn
5. Chao Zhang
6. Jonathan Pila
7. Xuhua He
8. E. Lau

In Mathematical Physics

1. Paul Ziegler
2. R. Pink
3. M. Hoff
4. T. Wedhorn
5. Chao Zhang
6. Xuhua He
7. E. Lau

Citations in the corpus

• $F$-zips with additional structure (2012, background): “ange for a ring homomorphism R→ R′. One obtains the category Dispn,d 1 of level 1 displays of height nand dimension dfibered over the category of Fp-algebras. This is a smooth algebraic stack over Fp ([10] Proposition 3.15). To every display D = (P,Q,ι,ε,F,F1) of level 1 of height nand dimension dove”
• Stack (2020, methodology): “…Fil : Pair (•) Lau → Vect (•) in Stack∨,N defined in same way as in Definition 2.8 and objects in the category Disp (m) Lau(R) can be described as tuples (M,F div) consisting of M ∈ Pair (m) Lau(R) and an isomorphism F div : σ- Fil(M) → M in Vect(m)(R), see [Lau10, Paragraph after Definition 3.4].”