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Frobenius Theorem and Structure of Morphisms / Gabriel Demazure.
Material type:
TextLanguage: English Publication details: UK : Phoenix Publication, 2023.Edition: 1st edDescription: xiii, 275 p. : 24 cmISBN: - 9789392359378
- 512.55 DEM
Contents:
Summary: This book presents a rigorous study of the Frobenius morphism, one of the central tools in algebraic geometry over fields of positive characteristic. It explains how the Frobenius map influences the structure of algebraic varieties and morphisms between schemes, and develops the theoretical framework needed to analyze finite, separable, and inseparable morphisms. The text explores the relationship between the Frobenius morphism and geometric properties such as smoothness, étaleness, and ramification, illustrating how these concepts are used to understand the behavior of algebraic objects in characteristic p.
Designed for graduate students and researchers, the book combines foundational theory with modern applications in algebraic geometry and commutative algebra. It provides detailed proofs, examples, and discussions that highlight the importance of Frobenius techniques in the study of algebraic groups, varieties, and scheme morphisms, making it a valuable reference for advanced mathematical research.
Z/2Z- graded linear algebra. Sheaves, functors and the geometric point of view. Supergeometry. Differentiable supermanifolds. The local structure of morphisms. Super Lie groups. Actions of Super Lie groups. Algebraic supergroups.
| Item type | Current library | Collection | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 512.55 DEM;2 (Browse shelf(Opens below)) | Available | 315604 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH-REFERENCE BOOKS | மூன்றாம் தளம் / Third floor | 512.55 DEM (Browse shelf(Opens below)) | Available | 315602 | |
| English Books | Kalaignar Centenary Library Madurai | ENGLISH - LENDING BOOKS | மூன்றாம் தளம் / Third floor | 512.55 DEM;1 (Browse shelf(Opens below)) | Available | 315603 |
Includes index.
Z/2Z- graded linear algebra. Sheaves, functors and the geometric point of view. Supergeometry. Differentiable supermanifolds. The local structure of morphisms. Super Lie groups. Actions of Super Lie groups. Algebraic supergroups.
This book presents a rigorous study of the Frobenius morphism, one of the central tools in algebraic geometry over fields of positive characteristic. It explains how the Frobenius map influences the structure of algebraic varieties and morphisms between schemes, and develops the theoretical framework needed to analyze finite, separable, and inseparable morphisms. The text explores the relationship between the Frobenius morphism and geometric properties such as smoothness, étaleness, and ramification, illustrating how these concepts are used to understand the behavior of algebraic objects in characteristic p.
Designed for graduate students and researchers, the book combines foundational theory with modern applications in algebraic geometry and commutative algebra. It provides detailed proofs, examples, and discussions that highlight the importance of Frobenius techniques in the study of algebraic groups, varieties, and scheme morphisms, making it a valuable reference for advanced mathematical research.