Simple morphisms in algebraic geometry / Richard Sot.

By: Sot, Richard, 1948-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 935.Publisher: Berlin ; New York : Springer-Verlag, 1982Description: 1 online resource (iv, 145 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540392651; 3540392653Subject(s): Geometry, Algebraic | Morphisms (Mathematics) | Géométrie analytique | Morphismes (Mathématiques) | Geometry, Algebraic | Morphisms (Mathematics) | Algebraische Geometrie | Einfacher Morphismus | MorphismusGenre/Form: Electronic books. Additional physical formats: Print version:: Simple morphisms in algebraic geometry.DDC classification: 516.35 LOC classification: QA3 | .L28 no. 935 | QA564Online resources: Click here to access online
Contents:
The Zariski topology, the Jacobian criterion and examples of simple algebras over a field k -- The Kahler 1-differentials -- Every k-algebra a which is essentially of finite type over k and simple is a regular local ring -- Brief discussion of unramified and étale homomorphisms -- Some corollaries to Theorem 3.5 -- Fitting ideals -- Proof of the Jacobian criterion and some characterizations of simple k-algebras and A-algebras -- Characterizations of simple A-algebras in terms of étale homomorphisms; invariance of the property of being a simple algebra under composition and change of base -- Descent of simple homomorphisms and removal of all noetherian assumptions in Chapter 7 and Chapter 8 -- Simple morphisms of preschemes and translation of previous theorems into the language of preschemes.
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Includes bibliographical references (page 145) and index.

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The Zariski topology, the Jacobian criterion and examples of simple algebras over a field k -- The Kahler 1-differentials -- Every k-algebra a which is essentially of finite type over k and simple is a regular local ring -- Brief discussion of unramified and étale homomorphisms -- Some corollaries to Theorem 3.5 -- Fitting ideals -- Proof of the Jacobian criterion and some characterizations of simple k-algebras and A-algebras -- Characterizations of simple A-algebras in terms of étale homomorphisms; invariance of the property of being a simple algebra under composition and change of base -- Descent of simple homomorphisms and removal of all noetherian assumptions in Chapter 7 and Chapter 8 -- Simple morphisms of preschemes and translation of previous theorems into the language of preschemes.

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