# Semiorthogonal Decompositions and Dimension

## Location

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Friday, December 10, 2021 12:00 PM

Noah Olander (Columbia University)

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.