System of points in saturated dg-categories

04/12/2016 - 16:00
04/12/2016 - 17:00
Michel Vaquié (Toulouse)

In this work we consider the question of realizing triangulated dg-categories by derived categories of algebraic varieties. For this, we introduce the notion of "system of points" in saturated dg-categories. We show that given such a system on a dg-category T, we can construct an algebraic space M, of finite type, smooth and separated, together with a dg-functor from T to a certain twisted dg-category of sheaves on M. We prove that this functor is furthermore an equivalence if and only if M is proper. All along this work we study t-strutcures on algebraic families of objects in T, which might be of independant interest.


(Joint work with Bertrand Toen)

Last edited by on Tue, 03/01/2016 - 00:09