**Contemporary Mathematics**

Volume: 79;
1988;
153 pp;
Softcover

MSC: Primary 14;
Secondary 13

Print ISBN: 978-0-8218-5085-5

Product Code: CONM/79

List Price: $29.00

Individual Member Price: $23.20

**Electronic ISBN: 978-0-8218-7667-1
Product Code: CONM/79.E**

List Price: $29.00

Individual Member Price: $23.20

# Regular Differential Forms

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*Ernst Kunz; Rolf Waldi*

This book is aimed at students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines. The book will provide readers with new insight into differential forms and may stimulate new research through the many open questions it raises.

The authors introduce various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms. It is known in many cases that the top degree regular differentials form a dualizing sheaf in the sense of duality theory. All constructions in the book are purely local and require only prerequisites from the theory of commutative noetherian rings and their Kähler differentials. The authors study the relations between the sheaves under consideration and give some applications to local properties of morphisms. The investigation of the “fundamental class,” a canonical homomorphism from Kähler to regular differential forms, is a major topic. The book closes with applications to curve singularities.

While regular differential forms have been previously studied mainly in the “absolute case” (that is, for algebraic varieties over fields), this book deals with the relative situation. Moreover, the authors strive to avoid “separability assumptions.” Once the construction of regular differential forms is given, many results can be transferred from the absolute to the relative case.

#### Table of Contents

# Table of Contents

## Regular Differential Forms

- Contents ix10 free
- Introduction 112 free
- §1. Integral differential forms 516
- §2. Ideals in noetherian rings having a prime basis 2435
- §3. Regular differential forms 4455
- §4. Complementary modules 6374
- §5. The fundamental class 91102
- §6. Applications to curve singularities 123134
- References 148159
- Corrigenda to [KD] 152163