We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.
We show that the Zink equivalence between -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic is compatible with duality. The proof relies on a new explicit formula for the -divisible group associated to a Dieudonné display.
Let K denote a number field, S a finite set of places of K, and ϕ: ℙⁿ → ℙⁿ a rational morphism defined over K. The main result of this paper states that there are only finitely many twists of ϕ defined over K which have good reduction at all places outside S. This answers a question of Silverman in the affirmative.
We construct a concrete example of a -parameter family of smooth projective geometrically integral varieties over an open subscheme of such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.