Bücher der Reihe New Mathematical Monographs

Hilbert's Tenth Problem - to find an algorithm to determine whether a polynomial equation in several variables with integer coefficients has integer solutions - was shown to be unsolvable in the late sixties. This book presents an account of results extending Hilbert's Tenth Problem to integrally closed subrings of global fields.

In this 2004 book, Cabanes and Enguehard blend many of the main concerns of modern algebra, with full proofs of some of the most remarkable achievements in the area. Three main themes are evident: first, applications of etale cohomology; second, the Dipper-James theorems; finally, local representation theory.