Remarks on generators and dimensions of triangulated categories

By Dmitri Orlov. 2008

151 citations recorded by the source corpus.

In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a9efd9270259a4eed860a8add5c113852633ac5a

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

On the derived category of the classical Godeaux surface (2012, background): “By Theorem 4 of [30] one may obtain a strong generator of A by projecting OX⊕M⊕M(2) into A, where M is a very ample line bundle on X.”
A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, background): “is equal to the Rouquier dimension of Db(mod−(A d1−1 ⊗k ···⊗k Adn−1)). As mentioned above, for any smooth algebraic curve, the bounded derived category of coherent sheaves has Rouquier dimension one, [Orl09b], however, the above argument shows that the category of matrix factorizations of a Fermat c”
Homological mirror symmetry for the 4-torus (2009, unknown): “so the valuation of the holonomy corresponds formally to translating the underlying Lagrangian by the corresponding flux, compare [ Au09 , Section 4.1] for the convergent case.”
Orlov spectra: bounds and gaps (2010, background): “Hence, O(p− q) can not be obtained in one step as it can not be obtained from O(3e) alone (this is the argument from [43]).”
Dynamical systems and categories (2013, unknown): “BothG andG∗ are generators ofDb(X) by [41].”