Grothendieck's localization problem
Takumi Murayama (Princeton University)
Abstract: Let $f\colon Y \rightarrow X$ be a proper flat morphism of algebraic varieties. Grothendieck and Dieudonné showed that the smoothness of $f$ can be detected at closed points of $X$. Using André–Quillen homology, André 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 singularities due to Gabber. Our method gives a uniform treatment of Grothendieck's localization problem and resolves various new cases of this problem, which asks whether similar statements hold for other local properties of morphisms.
The discussion for Takumi Murayama’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-01-22-tm (and will be deleted after ~3-7 days).
Audience: researchers in the topic
( paper )
Series comments: This seminar requires both advance registration, and a password. Register at stanford.zoom.us/meeting/register/tJEvcOuprz8vHtbL2_TTgZzr-_UhGvnr1EGv Password: 362880
If you have registered once, you are always registered, and can just join the talk. Link for talk once registered: in your email, or else probably: stanford.zoom.us/j/95272114542
More seminar information (including slides and videos, when available): agstanford.com
|*contact for this listing|