Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.

Erudite, insightful, thought-provoking, "Generalized Serre-Tate Ordinary Theory" is highly recommended for academic library Mathematic Studies reference collections and the supplemental reading lists for students and researchers working with arithmetic algebraic geometry and number theory.

To solve the Fermat problem, Miyaoka, a specialist in algebraic geometry, which concerns the relationship between geometric surfaces and solutions of equations, ventured into a relatively new field known as arithmetic algebraic geometry.