Smoothness of the truncated display functor

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.Comment: 38 page

Frames and finite group schemes over complete regular local rings

Let p be an odd prime. We show that the classification of p-divisible groups by Breuil windows and the classification of finite flat group schemes of p-power order by Breuil modules hold over any complete regular local ring with perfect residue field of characteristic p. We use a formalism of frames and windows with an abstract deformation theory that applies to Breuil windows.Comment: 22 page

A note on the dynamical zeta function of general toral endomorphisms

It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an elementary proof of this fact that extends to the case of general toral endomorphisms without change. The result is a closed formula that can be calculated by integer arithmetic only. We also address the functional equation and the relation between the Artin-Mazur and Lefschetz zeta functions.Comment: 8 pages; revised and slightly expanded versio

The Balmer spectrum of certain Deligne-Mumford stacks

We consider a Deligne-Mumford stack $X$ which is the quotient of an affine scheme $\operatorname{Spec}A$ by the action of a finite group $G$. If the ring $A$ is regular, the Balmer spectrum of the tensor triangulated category of perfect complexes on $X$ is homeomorphic to the space of homogeneous prime ideals in the group cohomology ring $H^*(G,A)$.Comment: 31 page

A relation between Dieudonne displays and crystalline Dieudonne theory

We discuss the relation between crystalline Dieudonne theory and Dieudonne displays, with special emphasis on the case p=2. The theory of Dieudonne displays is extended to this case without restriction, which implies that the classification of finite flat group schemes by Breuil-Kisin modules holds for p=2 as well.Comment: 47 pages, final versio

A duality theorem for Dieudonne displays

We show that the Zink equivalence between p-divisible groups and Dieudonne displays over a complete local ring with perfect residue field of characteristic p is compatible with duality. The proof relies on a new explicit formula for the p-divisible group associated to a Dieudonne display.Comment: 16 page