This week, Thursday at 11:00, U. Haifa Topology & Geometry seminar on January 16, 2020
Geometry & Topology Seminar
Speaker: Reconstruction of formal schemes using their derived categories
Topic: Saurabh Singh (Ben-Gurion)
Place: Room 614 in the Science & Education Building
Time: 11:00
Date: Thursday, January 16, 2020
Abstract:
We give a faithful embedding of the category of separated (or of finite Krull
dimension) noetherian formal schemes into the category of tensor triangulated
categories with unit. This can be viewed as a generalization of the work of Paul
Balmer over ordinary schemes where he uses the category of perfect complexes
to give an embedding. Over noetherian formal schemes, it is more convenient to
use the derived category Dqct( ) of modules whose homologies are quasi-coherent
and torsion. In this context, we use the classification of localizing subcategories of
Dqct(X) for a noetherian formal scheme X, as given by Leovigildo Alonso Tarrio,
Ana Jeremiaz Lopez and Maria Jose Souto Salorio to define the topological space
Spc(Dqct(X)) called the spectrum of Dqct(X). We show that there is a natural
ringed structure and an adic structure on Spc(Dqct(X)) which makes it into a
formal scheme and Spc(Dqct(X)) = X.
