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SUMMARY:Takumi Murayama (Princeton University)
DTSTART;VALUE=DATE-TIME:20210122T200000Z
DTEND;VALUE=DATE-TIME:20210122T210000Z
DTSTAMP;VALUE=DATE-TIME:20211209T075959Z
UID:agstanford/34
DESCRIPTION:Title: Grothendieck's localization problem\nby Takumi Murayama (Princeton
University) as part of Stanford algebraic geometry seminar\n\n\nAbstract\
nLet $f\\colon Y \\rightarrow X$ be a proper flat morphism of algebraic v
arieties. Grothendieck and Dieudonné showed that the smoothness of $f$ ca
n be detected at closed points of $X$. Using André–Quillen homology\, A
ndré showed that when $X$ is excellent\, the same conclusion holds when $
f$ is a closed flat morphism between locally noetherian schemes. We give a
new proof of André's result using a version of resolutions of singularit
ies due to Gabber. Our method gives a uniform treatment of Grothendieck's
localization problem and resolves various new cases of this problem\, whic
h asks whether similar statements hold for other local properties of morph
isms.\n
LOCATION:https://researchseminars.org/talk/agstanford/34/
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