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Let $X,Y$ be noetherian schemes and $f: X \rightarrow Y$ a morphism. What does (besides of the definition) the property finite imply. Can one make any conclusions like: dominant, birational, isomorphic on open subsets,...?

Thanks and greetings from Torrance

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    Finite morphisms are proper, so, e.g. universally closed. Closed immersions are finite, so finite morphisms definitely don't have to be dominant.2012-11-13
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    Finite is equivalent to "proper and affine". For example, a variety is at the same time proper and affine if and only if it has dimension zero.2012-11-13

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