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


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.