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A deformation of commutative polynomial algebras in even numbers of variables

Wenhua Zhao (2010)

Open Mathematics

We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture...

A descent map for curves with totally degenerate semi-stable reduction

Shahed Sharif (2013)

Journal de Théorie des Nombres de Bordeaux

Let K be a local field of residue characteristic p . Let C be a curve over K whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- p rational torsion subgroup on the Jacobian of C . We also determine divisibility of line bundles on C , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of C .

A description based on Schubert classes of cohomology of flag manifolds

Masaki Nakagawa (2008)

Fundamenta Mathematicae

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.

A dimension formula for Ekedahl-Oort strata

Ben Moonen (2004)

Annales de l’institut Fourier

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.

A duality theorem for Dieudonné displays

Eike Lau (2009)

Annales scientifiques de l'École Normale Supérieure

We show that the Zink equivalence between p -divisible groups and Dieudonné 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 Dieudonné display.

A dynamical Shafarevich theorem for twists of rational morphisms

Brian Justin Stout (2014)

Acta Arithmetica

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.

A family of varieties with exactly one pointless rational fiber

Bianca Viray (2010)

Journal de Théorie des Nombres de Bordeaux

We construct a concrete example of a 1 -parameter family of smooth projective geometrically integral varieties over an open subscheme of ℙ ℚ 1 such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.

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