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. We also study t-strutcures on algebraic families of

objects in T, which might be of independent interest.

### Homological Mirror Symmetry

Monday, February 20, 2017 - 12:00pm

#### Michel Vaquie

University of Toulouse