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Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtl

Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithm

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harr

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By de

The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his wor