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Picard groups of derived categories

✍ Scribed by H. Fausk

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 147 KB
Volume: 180
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00145-7

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✦ Synopsis

We investigate the group Pic(DM) of isomorphism classes of invertible objects in the derived category of O-modules for a commutative unital ringed Grothendieck topos (E;O) with enough points. When the ring Op has connected prime ideal spectrum for all points p of E we show that Pic(D M ) is naturally isomorphic to the Cartesian product of the Picard group of O-modules and the additive group of continuous functions from the space of isomorphism classes of points of E to the integers Z. Also, for a commutative unital ring R, the group Pic(DR) is isomorphic to the Cartesian product of Pic(R) and the additive group of continuous functions from spec R to the integers Z.

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