Let R be the homogeneous coordinate ring of Grassmannian G=Gr(2,n) defined over an algebraically closed field k characteristic p≥max⁡{n−2,3}. In this paper we give a description decomposition R, considered as graded Rpr-module, for r≥2. This is companion to [16], where case r=1 was treated, and taken together, our results imply that has finite F-representation type (FFRT). Though it expected al...

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose ‘lifts’ to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize p...

We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let φ : C̃ → C be an unramified morphism of non-singular plane projective curves defined over a number field K. We calculate an effective upper bound for the norm of the relative discriminant of the number field K(Q) over K for any point P ∈ C(K) and Q ∈ φ(P ). 2000 MCS: 14G25, 14H25, 11G30.

We prove a direct image theorem stating that the direct image of a Galois formula by a morphism of difference schemes is equivalent to a Galois formula modulo the theory ACFA of existentially closed difference fields. As a consequence, we obtain an effective quantifier elimination procedure and a precise algebraic-geometric description of definable sets over existentially closed difference fiel...

Let h:X → Y be a finite morphism of smooth connected complete curves over Cp. We show h extends to a finite morphism between semi-stable models of X and Y . 2000 Mathematics Subject Classification: 11G20

Many important systems such as concurrent heap-manipulating programs, communication networks, or distributed algorithms, are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation for the states of these systems, where transitions can be conveniently described by graph transformation rules. We present a framework for the abstraction of graphs sup...