The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of coherent sheaves on a smooth projective variety X of dimension n in n steps, we also provide an effective bound on the power of the ample line bundle needed to generate the bounded derived category of coherent sheaves on X in 2n - 1 steps. We also show that for a smooth projective toric variety X of dimension n over an arbitrary algebraically closed field, the Rouquier dimension of the bounded derived category of coherent sheaves on X is less or equal than 2n - 1. We also study derived categories of coherent D-modules on smooth projective varieties. We describe the subcategory of proper objects in the bounded derived category of coherent D-modules on a smooth projective variety X, and as a consequence we obtain that several geometric invariants of X are determined by the bounded derived category of coherent D-modules on X.

Creator

• Khromenkov, Yaroslav

DOI

• https://doi.org/10.21985/n2-tf5z-7865

Subject

• Mathematics
• Theoretical mathematics

Language

• en

Alternate Identifier

• etdadmin_upload_1004198
• http://dissertations.umi.com/northwestern:16672

Keyword

• Derived Categories
• Rouquier Dimension
• Algebraic Geometry

Date created

• 2023-01-01

Resource type

• Dissertation

Rights statement

• In Copyright