On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme

Tarrío, Leovigildo Alonso; López, Ana Jeremías; Rodríguez, Marta Pérez; Gonsalves, María Jesús Vale

doi:10.1007/s10485-009-9204-5

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…Moreover if is tamely compactly generated and has a single compact generator, then so is . This formulation is well suited to give examples of applications of Theorem 4.29 given by formal schemes and by -algebroid stacks on a smooth complex variety, recovering the existence of single compact generators from [AJPV11] and of [Pet12] respectively. Nilpotent deformations will also allow us to give a comparison with the work of Lowen and Van den Bergh [LB15] on the curvature problem.…”

Section: Generators and Curvature In Deformations Of Categoriesmentioning

confidence: 99%

Generators in formal deformations of categories

Blanc¹,

Katzarkov²,

Pandit³

2018

Compositio Math.

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In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a k-linear ∞-category for a field k. Our main result states that if C is a k-linear ∞-category which has a compact generator whose groups of self extensions vanish for sufficiently high positive degrees, then every formal deformation of C has zero curvature and moreover admits a compact generator.

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Section: Generators and Curvature In Deformations Of Categoriesmentioning

confidence: 99%

Generators in formal deformations of categories

Blanc¹,

Katzarkov²,

Pandit³

2018

Compositio Math.

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Hochster duality in derived categories and point-free reconstruction of schemes

Kock¹,

Pitsch²

2016

Trans. Amer. Math. Soc.

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For a commutative ring R, we exploit localization techniques and point-free topology to give an explicit realization of both the Zariski frame of R (the frame of radical ideals in R) and its Hochster dual frame, as lattices in the poset of localizing subcategories of the unbounded derived category D(R). This yields new conceptual proofs of the classical theorems of Hopkins-Neeman and Thomason. Next we revisit and simplify Balmer's theory of spectra and supports for tensor triangulated categories from the viewpoint of frames and Hochster duality. Finally we exploit our results to show how a coherent scheme (X, O X ) can be reconstructed from the tensor triangulated structure of its derived category of perfect complexes.

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On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme

Cited by 2 publications

References 16 publications

Generators in formal deformations of categories

Generators in formal deformations of categories

Hochster duality in derived categories and point-free reconstruction of schemes

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