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Rouquier dimension and approximation by perfect complexes
Algebraic Geometry and Number Theory| Speaker: | Noah Olander, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Thu, Apr 24 2025, 1:10PM |
In 2003, Rouquier introduced an important notion of dimension for triangulated categories. If X is a quasi-projective variety over an algebraically closed field and X is not smooth, then the Rouquier dimension of the category of perfect complexes (bounded complexes of vector bundles) on X is infinite, while the Rouquier dimension of the bounded derived category of coherent sheaves is finite. I will explain that nevertheless, the latter number can be computed in terms of perfect complexes. I will give some examples to show that this is useful due to the nice homological properties of vector bundles. This is joint work with Pat Lank.