We give a classification of all possible 2-adic images of Galois representations associated to elliptic curves over Q. To this end, we compute the ‘arithmetically maximal’ tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.

Here we study the gonality of several projective curves which arise in a natural way (e.g. curves with maximal genus in Pn, curves with given degree d and genus g for all possible d, g if n = 3 and with large g for arbitrary (d, g, n)).

1. Forced exhalations performed from volumes below total lung capacity, so-called partial expiratory flow-volume curves, are suggested to be more sensitive in detecting airways bronchoconstriction than maximal expiratory flow-volume curves begun at total lung capacity. 2. In eight healthy men both maximal and partial expiratory flow-volume curves were measured where breath was held at total lun...

A new family of Fq2-maximal curves is presented and some of their properties are investigated.

Extending results for space curves we establish bounds for the cohomology of a non-degenerate curve in projective n-space. As a consequence, for any given n we determine all possible pairs (d, g) where d is the degree and g is the (arithmetic) genus of the curve. Furthermore, we show that curves attaining our bounds always exist and describe properties of these extremal curves. In particular, w...