The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map.

Review of the hardback:‘… a well-motivated survey of such a broad range of material, some of it quite technical, which leads the reader to the forefront of some of the deepest modern developments in Intersection Theory.’

Source: Proceedings of the Edinburgh Mathematical Society