Download Algebraic Surfaces by Oscar Zariski PDF

By Oscar Zariski

The most target of this e-book is to offer a very algebraic method of the Enriques¿ category of tender projective surfaces outlined over an algebraically closed box of arbitrary attribute. This algebraic technique is likely one of the novelties of this booklet one of the different glossy textbooks dedicated to this topic. chapters on floor singularities also are integrated. The e-book may be beneficial as a textbook for a graduate direction on surfaces, for researchers or graduate scholars in algebraic geometry, in addition to these mathematicians operating in algebraic geometry or comparable fields"

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1. — Supposons que tp : Xp → Yp soit un isomorphisme pour p ≤ n. Alors, pour tout Faisceau F de SF , et at induit un isomorphisme ∼ τ

5. — Supposons que pour tout n, les fl`eches Xn+1 → cosqn (X)n+1 soient de S-descente cohomologique universelle. Alors, X → S est de descente cohomologique universelle. DESCENTE COHOMOLOGIQUE 33 D´emonstration. 2, les fl`eches cosqn+1 (X)p → cosqn (X)p sont des ´equivalences de descente cohomologique pour tout p. 1.

On peut supposer p > n + 1. On ´ecrit alors cosqn+1 (X)p = lim Xq ←− [q]→[p] q≤n+1 comme le noyau de la double fl`eche ΠX = d´ ef Xq ⇒ Xi = ΞX α [q]→[p] q≤n+1 [i] →[j] [p] j≤n+1 o` u la composante αX d’indice α ∈ Hom[p] ([i], [j]) de la double fl`eche est la double fl`eche form´ee d’une part du morphisme ΠX → Xi de projection d’indice [i] → [p] et, d’autre part, du morphisme ΠX → Xj → Xi , compos´e de la projection d’indice [j] → [p] et de α ∈ Hom(Xj , Xi ). 3. — Soit p un entier naturel. Le diagramme / ΠX cosqn+1 (X)p  ˜ p cosqn+1 (X) /  ˜ ΠX est cart´esien.

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