We have carried out a genome screen for atopic dermatitis (AD) and have identified linkage to AD on chromosomes 1q21, 17q25 and 20p. These regions correspond closely with known psoriasis loci, as does a previously identified AD locus on chromosome 3q21. The results indicate that AD is influenced by genes with general effects on dermal inflammation and immunity.

0. Introduction. By the Mordell-Weil rank of a curve over a number field we mean the rank of the group of points on its Jacobian. In his paper Sur les points rationels des courbes algebriques de genre supbrieur ?t l'unitb, Chabauty showed that a curve of genus g over a number field with Mordell-Weil rank at most g has finitely many points. This result is now superceded by Falting's work. However, as we shall show in this note, Chabauty's method can be used to give good effective bounds for the number of points on a curve as above. For example, we will show: (i) A curve of genus two over Q with good reduction at two or three and Mordell-Weil rank at most one has at most twelve rational points.More generally, (ii) Suppose C is a curve of genus g over a number field K with Mordell-Weil rank at most g-1. Suppose is an unramified prime of K at which C has good reduction, of residue characteristic strictly greater than 2g. Then # C(K)< N + 2g(N + 1)-1.Turning the method around we can show:

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