The notion of a prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares these prolongation spaces with algebraic jet spaces is introduced and studied.

In a recently performed monitoring project, 18 OCPs (Organochlorine pesticides) in paired samples of pine needles and human breast milk samples were analysed in different regions in the Taurus Mountains in Turkey. The aim of our data evaluation approach is to find out whether there are conformities between the paired human breast milk and pine needle samples. An appropriate data analysis method...

Br(X)/Br0(X)×X(Ak) → Q/Z. We shall call this the Brauer–Manin pairing. Let us define X(Ak) Br as “the right kernel” of this pairing, that is, the subset of points of X(Ak) orthogonal to all elements of Br(X). Manin made an important observation that by the global reciprocity law the image ofX(k) under the diagonal embedding X(k) →֒ X(Ak) is contained in X(Ak) . A variety X such that X(Ak) 6= ∅ w...

Lattice diagrams, known as Hasse diagrams, have played an ever increasing role in lattice theory and fields that use lattices as a tool. Initially regarded with suspicion, they now play an important role in both pure lattice theory and in data representation. Now that lattices can be created by software, it is important to have software that can automatically draw them. This paper covers: – The...

We study the existence of rational points on modular curves of D-elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some applications which include finding presentations for arithmetic groups arising from quaternion algebras, finding the equations of modular curves of D-elliptic sheaves, and constructing curves violating the Hasse principle.

For any Boolean algebra we prove a nice-looking recursive formula for the characteristic polynomial of its associated undirected Hasse graph, from which the computation of the spectrum smoothly follows.

The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the i...

Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse’s unit...