1 “...; both graduate students and professional number theorists will find this an ideal introduction. Material...”

2 “... and an arithmetic Riemann-Roch theorem. To aid number theorists, background material on differential geometry...”

3 “...Diophantine geometry has been studied by number theorists for thousands of years, since the time...”

4 “... algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists...”

5 “... to number theorists and algebraic geometers; because of applications of the theory, it may also...”

6 “.... It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists...”