Picard groups of derived categories

Fausk, Halvard

doi:10.1016/s0022-4049(02)00145-7

Cited by 12 publications

(9 citation statements)

References 6 publications

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“…REMARK 6.5 The result is the same if one works with bigger derived categories instead of D perf (X). See for instance Fausk's paper [6]. This might look more general than the above Proposition but one should keep in mind that invertible objects in such big categories are necessarily compact, just by abstract non-sense, see [7,Proposition A.2.8] for instance.…”

Section: Lemma 62 An Object a In K Is Invertible If And Only If It Imentioning

confidence: 94%

Gluing Techniques in Triangular Geometry

Balmer¹,

Favi²

2007

The Quarterly Journal of Mathematics

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Section: Lemma 62 An Object a In K Is Invertible If And Only If It Imentioning

confidence: 94%

Gluing Techniques in Triangular Geometry

Balmer¹,

Favi²

2007

The Quarterly Journal of Mathematics

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“…(i) for the case where R is decomposable. This computation was originally established in [11]. Although Fausk did not use weight structures, one observes that by applying our arguments (see §5) to the triangulated category D c (R), equipped with the weight structure whose heart consists of the finitely generated projective R-modules, one obtains a reasoning somewhat similar to his one.…”

Section: Under Assumptions (B1)-(b2) We Havementioning

confidence: 64%

Picard groups, weight structures, and (noncommutative) mixed motives

Bondarko¹,

Tabuada²

2015

Preprint

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We develop a general theory which enables the computation of the Picard group of a symmetric monoidal triangulated category, equipped with a weight structure, in terms of the Picard group of the associated heart. As an application, we compute the Picard group of several categories of motivic nature -mixed Artin motives, mixed Artin-Tate motives, motivic spectra, noncommutative mixed Artin motives, noncommutative mixed motives of central simple algebras, noncommutative mixed motives of separable algebras -as well as the Picard group of the derived categories of symmetric ring spectra.

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“…This shows that Pic(M R ) coincides with Pic(R) as defined classically. In fact, for any scheme X, our Pic(sh(X)) is isomorphic to Pic(X) as defined classically [17,II.6.12]; see [10].…”

Section: Proof Since the Functor ( − )mentioning

confidence: 99%

“…The Picard groups of the derived categories D R and of the analogous derived categories of sheaves of modules have been calculated by Fausk [10].…”

Section: Proof Since the Functor ( − )mentioning

confidence: 99%