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Volume I Arithmetic.- Generators of the N¿n-Severi Group of a Fermat Surface.- p-adic Etale Cohomology.- The Mordell-Weil Group of Curves of Genus 2.- Number Theoretic Applications of Polynomials with Rational Coefficients Defined by Extremality Conditions.- Infinite Descent on Elliptic Curves with Complex Multiplication.- On the Ubiquity of Pathology in Products.- Conjectured Diophantine Estimates on Elliptic Curves.- Zeta-Functions of Varieties over Finite Fields at s =1.- Canonical Height Pairings via Biextensions.- The Action of an Automorphism of C on a Shimura Variety and its Special Points.- The Torelli Theorem for Ordinary K3 Surfaces over Finite Fields.- Real Points on Shimura Curves.- Special Automorphic Forms on PGSp4.- Courbes sur une vari¿ ab¿enne et points de torsion.- Euler and the Jacobians of Elliptic Curves.