Springer Monographs in Mathematics

4 total works

Galois Cohomology

by Jean-Pierre Serre

Published 1 August 1997

This is an updated English translation of "Cohomologie Galoisien-ne" published more than 30 years ago, as one of the very first "Lecture Notes in Mathematics". It includes a reproduction of an influential paper of R. Steinberg, together with some new material and an expanded bibliography.

Complex Semisimple Lie Algebras

by Jean-Pierre Serre

Published 23 October 1987

These short notes, already well-known in their original French edition, present the basic theory of semisimple Lie algebras over the complex numbers. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups. The book is intended to guide the reader towards further study.

Trees

by Jean-Pierre Serre

Published 1 October 1980

From the reviews:

"Serre's notes on groups acting on trees have appeared in various forms (all in French) over the past ten years and they have had a profound influence on the development of many areas, for example, the theory of ends of discrete groups. This fine translation is very welcome and I strongly recommend it as an introduction to an important subject. In Chapter I, which is self-contained, the pace is fairly gentle. The author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the (rather difficult) proof of the general case." (A.W. Mason in Proceedings of the Edinburgh Mathematical Society 1982)

Local Algebra

by Jean-Pierre Serre

Published 16 June 2000

This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.