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arXiv · 2110.09256

Fully Faithful Functors and Dimension

Noah Olander
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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 $D^b_{coh}(X) \subset D^b_{coh}(Y)$ with $X, Y$ smooth proper varieties, then $\mathrm{dim}(X) \leq \mathrm{dim}(Y)$.

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Noah Olander. 2021-09-23. Fully Faithful Functors and Dimension. https://arxiv.org/abs/2110.09256

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