Characterising elliptic solids of Q(4,q), q even

Elliptic Curves over Q

All polynomials and rational functions in this essay are assumed to have coefficients in Q . Fix an integer n ≥ 1. An affine variety is a simultaneous irreducible system of polynomial equations in n variables. The Q -points, R -points and C points of the affine variety are all solutions of the polynomial system in Q , R n and C , respectively. Rational projective n-spaceg Q n is the set of line...

Elliptic Curves over Q

Quasi-Hermitian varieties in PG(r, q^2), q even

In this paper a new example of quasi–Hermitian variety V in PG(r, q) is provided, where q is an odd power of 2. In higherdimensional spaces, V can be viewed as a generalization of the Buekenhout-Tits unital in the desarguesian projective plane; see [9].

Elementary Elliptic (r, Q)-polycycles

We consider the following generalization of the decomposition theorem for polycycles. A (R, q)-polycycle is, roughly, a plane graph, whose faces, besides some disjoint holes, are i-gons, i ∈ R, and whose vertices, outside of holes, are q-valent. Such polycycle is called elliptic, parabolic or hyperbolic if 1 q + 1 r − 1 2 (where r = maxi∈Ri) is positive, zero or negative, respectively. An edge ...

ELLIPTIC CURVES OVER Q(i)

A study of the diophantine equation v2 = 2u4 − 1 led the authors to consider elliptic curves specifically over Q(i) and to examine the parallels and differences with the classical theory over Q. In this paper we present some extensions of the classical theory along with some examples illustrating the results. The well-known diophantine equation v2 = 2u4 − 1 , has, ignoring signs, only two integ...