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Regular Differential Forms
 
Front Cover for Regular Differential Forms
Available Formats:
Electronic ISBN: 978-0-8218-7667-1
Product Code: CONM/79.E
List Price: $29.00
MAA Member Price: $26.10
AMS Member Price: $23.20
Front Cover for Regular Differential Forms
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Regular Differential Forms
Available Formats:
Electronic ISBN:  978-0-8218-7667-1
Product Code:  CONM/79.E
List Price: $29.00
MAA Member Price: $26.10
AMS Member Price: $23.20
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 791988; 153 pp
    MSC: Primary 14; Secondary 13;

    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
     
     
    • Chapters
    • Introduction
    • §1. Integral differential forms
    • §2. Ideals in noetherian rings having a prime basis
    • §3. Regular differential forms
    • §4. Complementary modules
    • §5. The fundamental class
    • §6. Applications to curve singularities
    • References
    • Corrigenda to [KD]
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Volume: 791988; 153 pp
MSC: Primary 14; Secondary 13;

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.

  • Chapters
  • Introduction
  • §1. Integral differential forms
  • §2. Ideals in noetherian rings having a prime basis
  • §3. Regular differential forms
  • §4. Complementary modules
  • §5. The fundamental class
  • §6. Applications to curve singularities
  • References
  • Corrigenda to [KD]
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