/sci/ - Science & Math

>this thread

Suppose we have a proper flat morphism <span class="math">f:X \to Y[/spoiler] over <span class="math">k[/spoiler]. For an arbitrary point <span class="math">y \in Y[/spoiler], the fiber <span class="math">X_{y}[/spoiler] is considered smooth on <span class="math">k(y)[/spoiler]. Prove that there is an open neighborhood <span class="math">U[/spoiler] of <span class="math">y[/spoiler] in <span class="math">Y[/spoiler] so we have <span class="math">f:f^{-1}(U) \to U[/spoiler] be smooth.

This should be easy, but after writing a paper I am shooting blanks. I know there's some faggots who know math on here (I got help the last time), so I might as well try here before I go to Stackexchange and wait four hours to get a response. Any suggestions?