2011, ISBN: 9780821876671

eBooks, eBook Download (PDF), This book is aimed at students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines. The book will provide readers with ne… Mehr…

eBooks, eBook Download (PDF), 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 Kaehler differentials. The authors study the relations between the sheaves under consideration and give some applications to local properties of morphisms. The investigation of the &quote;fundamental class,&quote; a canonical homomorphism from Kaehler 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 &quote;absolute case&quote; (that is, for algebraic varieties over fields), this book deals with the relative situation. Moreover, the authors strive to avoid &quote;separability assumptions.&quote; Once the construction of regular differential forms is given, many results can be transferred from the absolute to the relative case. [PU: American Mathematical Society], Seiten: 153, American Mathematical Society, 2011<

ISBN: 9780821876671

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 for… Mehr…

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 Kaehler 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 Kaehler 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. ; PDF; Scientific, Technical and Medical > Mathematics > Algebra, American Mathematical Society<

ISBN: 9780821876671

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 for… Mehr…

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 Kaehler 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 Kaehler 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. ; PDF; Scientific, Technical and Medical > Mathematics > Algebra, American Mathematical Society<

2011, ISBN: 9780821876671

eBooks, eBook Download (PDF), [PU: American Mathematical Society], American Mathematical Society, 2011