Grothendieck's localization problem

Takumi Murayama (Princeton University)

Fri Jan 22, 20:00-21:00 (5 weeks ago)

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 (and will be deleted after ~3-7 days).

algebraic geometry

Audience: researchers in the topic

( paper )

Stanford algebraic geometry seminar

Series comments: This seminar requires both advance registration, and a password. Register at 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:

More seminar information (including slides and videos, when available):

Organizer: Ravi Vakil*
*contact for this listing

Export talk to