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Homological Mirror Symmetry

Monday, February 20, 2017 - 12:00pm

Michel Vaquie

University of Toulouse


University of Pennsylvania

DRL 4N30

special time

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.

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