Twelve cases of leptospirosis followed by the Infectious Diseases Clinic of the Cukurova University Medical School, Adana, Turkey, between January 1994 and November 1995 are reported. Included are their clinical manifestation, laboratory findings and serotype. Nine men and three women with an average age of 40.4 years were studied. Symptoms, clinical manifestations, laboratory findings and trea...

In this chapter we will relate the topology of smooth projective varieties over the complex numbers with counting points over finite fields, via the Weil conjectures. If X is a variety defined over a finite field Fq, one can count its points over the various finite extensions of Fq; denote Nm = |X(Fmq )| (for instance, if X ⊂ AnFq is affine, given by equations f1, . . . , fk, then Nm = |{x ∈ Fm...

Introduction Hajdu-Cheney syndrome (HCS) is a rare autosomal dominant disease characterized by acroosteolysis, wormian skull bones with persistent skull sutures, premature loss of teeth, micrognathia, short stature, hypermobility of the joints, neurologic manifestations such as basilar invagination with subsequent paresthesia, hearing loss, and speech alterations, and osteoporosis with tendency...

Let A be a modular abelian variety of GL2-type over a totally real field F of class number one. Under some mild assumptions, we show that the Mordell-Weil rank of A grows polynomially over Hilbert class fields of CM extensions of F .

The starting point of this method is Falting’s article in which he proves the Mordell-Weil theorem. He remarked and Serre turned it into a working method, the fact that the equivalence of two λ-adic representations is something that can be basically determined on some finite extension of the base field (even though the representations might not factor through a finite quotient). Let Oλ be the r...

This paper assumes no background on elliptic curves and culminates with a proof of the Mordell-Weil theorem. The Riemann-Roch and Dirichlet unit theorem are recalled but used without proof, but everything else is self-contained. After some elementary properties of elliptic curves are given, the group structure is explored in detail.