Morphisme plat ( Flatness )

invite52487760 · 29/11/2015, 20h54

Bonsoir à tous,

- J'ai besoin qu'on m'indique un cours qui porte sur le sujet suivant ( même en anglais ) :

If $\text{[math]}$ is any morphism, with $\text{[math]}$ smooth and one-dimensional, then $\text{[math]}$ is flat over $\text{[math]}$ as long as no component of $\text{[math]}$ ( either irreducible or embedded ) is supported on the fiber $\text{[math]}$

Suppose that $\text{[math]}$ is an arbitrary morphism from a variety $\text{[math]}$ to a $\text{[math]}$ -dimensional smooth variety $\text{[math]}$ , and $\text{[math]}$ is a point. We define the limit $\text{[math]}$ of the family $\text{[math]}$ to be the fiber over $\text{[math]}$ in the closure $\text{[math]}$ . In these terms, the statement above says that a morphism $\text{[math]}$ to any smooth, one-dimensional target $\text{[math]}$ is flat if and only if every fiber $\text{[math]}$ is equal to the limit $\text{[math]}$

- Pouvez vous m'expliquer ce qu'on entend formellement par ce passage :

If $\text{[math]}$ is any morphism, with $\text{[math]}$ smooth and one-dimensional, then $\text{[math]}$ is flat over $\text{[math]}$ as long as no component of $\text{[math]}$ ( either irreducible or embedded ) is supported on the fiber $\text{[math]}$

Merci d'avance

Morphisme plat ( Flatness )

Morphisme plat ( Flatness )

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