On the Hodge-Newton filtration for p-divisible groups of Hodge type

A p-divisible group, or more generally an F-crystal, is said to be Hodge-Newton reducible if its Hodge polygon passes through a break point of its Newton polygon. Katz proved that Hodge-Newton reducible F-crystals admit a canonical filtration called the Hodge-Newton filtration. The notion of Hodge-Newton reducibility plays an important role in the deformation theory of p-divisible groups; the key property is that the Hodge-Newton filtration of a p-divisible group over a field of characteristic p can be uniquely lifted to a filtration of its deformation. We generalize Katz's result to F-crystals that arise from an unramified local Shimura datum of Hodge type. As an application, we give a generalization of Serre-Tate deformation theory for local Shimura data of Hodge type. We also apply our deformation theory to study some congruence relations on Shimura varieties of Hodge type.Comment: 31 page

Mixed Hodge Structures

With a basic knowledge of cohomology theory, the background necessary to understand Hodge theory and polarization, Deligne's Mixed Hodge Structure on cohomology of complex algebraic varieties is described.Comment: pages 8

The basic cohomology of the twisted N=16, D=2 super Maxwell theory

We consider a recently proposed two-dimensional Abelian model for a Hodge theory, which is neither a Witten type nor a Schwarz type topological theory. It is argued that this model is not a good candidate for a Hodge theory since, on-shell, the BRST Laplacian vanishes. We show, that this model allows for a natural extension such that the resulting topological theory is of Witten type and can be identified with the twisted N=16, D=2 super Maxwell theory. Furthermore, the underlying basic cohomology preserves the Hodge-type structure and, on-shell, the BRST Laplacian does not vanish.Comment: 9 pages, Latex; new Section 4 showing the invariants added; 2 references and relating remarks adde