Noah Olander (Dec. 10, 2021):  Semiorthogonal decompositions and dimension
Channel: Algebraic Geometry at Stanford
Date: 2021-12-13

A conjecture of Orlov predicts that we can recover the dimension of a smooth quasi-projective variety from its derived category via the Rouquier dimension. We explain the meaning of the conjecture and some things we know about it, then we explain the proof of a weakened version. We use this to prove a fact predicted by Orlov’s conjecture: If the derived category of X appears as a component of  a semiorthogonal decomposition of the derived category of Y (X,Y smooth proper varieties) then the dimension of X is at most the dimension of Y.