Не Нётер.
The only reason I assumed all the schemes are locally Noetherian was that I didn’t want
to keep saying finite presentation etc. for finite type. I can’t believe it really matters anywhere. The
fibre product schemes on p. 70, line 2, and p80 are not automatically Noetherian. If I remember
correctly, Grothendieck’s example of naturally arising nonnoetherian rings is the tensor product
of two completions of ring. Products of Henselizations are probably only about as Noetherian as
completions.

J. Milne.

Ненётеровы кольца ближе, чем можно было думать. ($k[[x]] \otimes_{k} k[[y]]$ ненётерово, как и $\Z_{p} \otimes_{\Z} \Z_{q}$).