Fully Faithful Functors and Dimension

Abstract

We define the countable Rouquier dimension of a triangulated category and use this notion together with Theorem 2 of [Ola21] to prove that if there is a fully faithful embedding $D_{coh}^b(X)\subset D_{coh}^b(Y)$ with $X,Y$ smooth proper varieties, then $\dim (X)\le \dim (Y)$.

2 pages, comments welcome

References in corpus (1)

• The Rouquier Dimension of Quasi-Affine Schemes