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Derived quot schemes

Ionuţ Ciocan-Fontanine, Mikhail Kapranov (2001)

Annales scientifiques de l'École Normale Supérieure

Des propriétés de finitude des foncteurs polynomiaux

Aurélien Djament (2016)

Fundamenta Mathematicae

We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...

Descent equivalence

Xiuzhan Guo, Manuela Sobral, Walter Tholen (2004)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Descent for monads.

Hofstra, Pieter, De Marchi, Federico (2006)

Theory and Applications of Categories [electronic only]

Determinantal Barlow surfaces and phantom categories

Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov, Pawel Sosna (2015)

Journal of the European Mathematical Society

We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of S in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom category....

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