Class Groups and Picard Groups of Group Rings and Orders

I. Reiner9780821816769, 0-8218-1676-4

The aim of the lectures is to provide an introduction to recent developments in the theory of class groups and Picard groups. The techniques employed come from the three main areas: algebraic number theory, representation theory of algebras and orders, and algebraic $K$-theory.

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Table of contents :
Class groups and Picard groups of group rings and orders……Page 1
Contents……Page 4
1. Introduction……Page 6
2. Explicit Formulas……Page 11
3. Change of Orders……Page 18
4. Class Groups of p-Groups……Page 23
5. Mayer-Vietoris Sequences……Page 25
6. Calculations……Page 29
7. Survey of Specific Results……Page 33
8. Induction Techniques……Page 36
9. Picard Groups……Page 40
References……Page 46
Index……Page 49