Regular Differential Forms

Regular Differential Forms

by Rolf Waldi, Ernst Kunz
     
 

ISBN-10: 0821850857

ISBN-13: 9780821850855

Pub. Date: 12/31/1988

Publisher: American Mathematical Society

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

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Overview

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 Kahler 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 Kahler 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.

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Product Details

ISBN-13:
9780821850855
Publisher:
American Mathematical Society
Publication date:
12/31/1988
Series:
Contemporary Mathematics Series, #79
Pages:
153

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