0
votes
0answers
138 views

How would you call a subscheme of a smooth $S$-scheme?

In my preprint I propose to call $X/S$ quasi-smooth if $X$ can be embedded into a smooth $X'/S$. Does this sound fine? Upd. So, smoothly embeddable is better? Is it ok to call a morphism smoothly ...
18
votes
1answer
879 views

Why and how did preschemes become schemes?

Originally (e.g., in the first edition of EGA and in Mumford's Red Book), what are now called "schemes" were referred to as "preschemes." The word "scheme" was reserved for what are now called ...
21
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0answers
2k views

Why “open immersion” rather than “open embedding”?

When topologists speak of an "immersion", they are quite deliberately describing something that is not necessarily an "embedding." But I cannot think of any use of the word "embedding" in algebraic ...