Nagata's compactification theorem
id:
nagata-s-compactification-theorem-302-13479896
title:
Nagata's compactification theorem
text:
In algebraic geometry, Nagata's compactification theorem, introduced by Nagata (1962, 1963), implies that every abstract variety can be embedded in a complete variety, and more generally shows that a separated and finite type morphism to a Noetherian scheme S can be factored into an open immersion followed by a proper morphism. Nagata's original proof used the older terminology of Zariski–Riemann spaces and valuation theory, which sometimes made it hard to follow.
Deligne showed, in unpublished
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https://en.wikipedia.org/wiki/Nagata%27s_compactification_theorem
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2024-04-19T01:27:06Z
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