Theses Doctoral

Resolutions, bounds, and dimensions for derived categories of varieties

Olander, Noah

In this thesis we solve three problems about derived categories of algebraic varieties: We prove the conjecture [EL21, Conjecture 4.13] of Elagin and Lunts; we positively answer a question raised by the conjecture [Orl09, Conjecture 10] of Orlov, proving new cases of that conjecture in the process; and we extend Orlov's theorem [Orl97, Theorem 2.2] from smooth projective varieties to smooth proper algebraic spaces.

These results go toward answering the questions: How rigid is the (triangulated) derived category of coherent sheaves on an algebraic variety, and how much information does it possess about the variety? Our techniques are general and work for algebraic spaces just as well as they do for projective varieties.


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More About This Work

Academic Units
Thesis Advisors
Jong, Aise Johan de
Ph.D., Columbia University
Published Here
April 20, 2022