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changed the statement and the proof 2014-02-01 476921c
Upgrade lemma-check-closed-infinitesimally Tag 0896

Ugly edit to make sure the lemma applies in the only spot it is used.
Really, we should add a bunch of results of the following kind. Given

X' ---> X
|       |
v       V
S' ---> S

a cartesian square of algebraic spaces or schemes where S' --> S is a
thickening and X' ---> S' satisfies P then X ---> S satisfies P.

This works for P="affine" in general and for
P="closed immersion", "finite", and more if the thickening has finite order
which is really the correct generality for the lemma (but it comes too early
in the stacks project so we can't use this terminology yet).
assigned tag 0896 2012-10-19 1ab02c4
Tags: added new tags
created statement with label lemma-check-closed-infinitesimally in morphisms.tex 2012-10-13 2d9d272
Grothendieck's algebraization theorem