Quadratic form schemes with non-trivial radical

Trivial Stable Structures with Non-trivial Reducts

We offer a new viewpoint on some of the generic structures constructed using Hrushovski’s predimensions and show that they are natural reducts of quite straightforward trivial, one-based stable structures. 2000 Mathematics Subject Classification: 03C45.

Rationally trivial quadratic spaces are locally trivial:III

It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R such that q(v) = 0. If char(R) = 2, then in the case of even n we assume that q is a non-singular space in the sense of [Kn] and...

Extensions of Raynaud Schemes with Trivial Generic Fibers

We calculate the number of extensions of Raynaud schemes over the ring of integers of an absolutely ramified p-adic field with the trivial generic fibers by counting the rational points of the moduli space of finite flat models. Introduction Let K be a totally ramified extension of degree e over Qp for p > 2, and F be a finite field of characteristic p. We consider the constant group scheme CF ...

Strongly regular graphs with non-trivial automorphisms

Some Non-trivial Cocycles

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...