Neron models were invented by A. Neron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Neron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Neron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Neron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Neron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Neron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.

NA(c)ron models were invented by A. NA(c)ron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of NA(c)ron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about NA(c)ron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of NA(c)ron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of NA(c)ron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between NA(c)ron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.

This volume contains detailed expositions of talks given during an instructional conference held at Luminy in December 1998, which was devoted to classical and recent results concerning the fundamental group of algebraic curves, especially over finite and local fields. The scientific guidance of the conference was supplied by M. Raynaud, a leading expert in the field. The purpose of this volume is twofold. Firstly, it gives an account of basic results concerning rigid geometry, stable curves, and algebraic fundamental groups, in a form which should make them largely accessible to graduate students mastering a basic course in modern algebraic geometry. However classic, most of this material has not appeared in book form yet. In particular, the semi-stable reduction theorem for curves is covered with special care, including various detailed proofs. Secondly, it presents self-contained expositions of important recent developments, including the work of Tamagawa on Grothendieck's anabelian conjecture for curves over finite fields, and the solution by Raynaud and Harbater of Abhyankar's conjecture about coverings of affine curves in positive characteristic. These expositions should be accessible to research students who have read the previous chapters. They are also aimed at experts in number theory and algebraic geometry who want to read a streamlined account of these recent advances.