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SUMMARY:Takumi Murayama (Princeton University)
DTSTART:20210122T200000Z
DTEND:20210122T210000Z
DTSTAMP:20260407T214655Z
UID:agstanford/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/3
 4/">Grothendieck's localization problem</a>\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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