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Let [math]X \in \operatorname{Sch} /k[/math].
Show the functor [math]{\operatorname{Def} _X}:\operatorname{Art} \left( {\Lambda ,k} \right) \to \operatorname{Set} [/math] given by...
[math]{\operatorname{Def} _X}\left( A \right) = \left\{ {\begin{array}{*{20}{c}}
X& \to &{{X_A}} \\
\downarrow &{Cartesian}&{\mathop \downarrow \limits_{flat} } \\
{\operatorname{Spec} k}& \to &{\operatorname{Spec} A}
\end{array}} \right\}/ \cong [/math]
is a deformation functor.
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>>8501700
do your own homework, underage fag
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>>8501745
but its hard
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>>8501700
It follows trivially from the definition brainlet
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>>8501700
I'll leave this as an exercise for the reader
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>>8501700
what are you having trouble on? I haven't studied deformations much but don't you just have to check some gluing conditions on infinitesimal neighborhoods or something
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>>8501700
>anything involving geometry/topology
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>>8501768
I believe this is what you are looking for http://math.stanford.edu/~vakil/727/class19.pdf
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>>8501768
>don't you just have to check some gluing conditions on infinitesimal neighborhoods
Yes but it is not straightforward.
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>observer
it all makes sense now
Thread posts: 10
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