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A note on secondary K-theory II

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arxiv 1607.03094 v3 pith:7DYFXJ5T submitted 2016-07-11 math.AG math.ATmath.KT

Goncalo Tabuada This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords casenotesecondarybrauercanonicalderivedinjectiveintegral
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This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the secondary Grothendieck ring has the following injectivity properties: in the case of a regular integral quasi-compact quasi-separated scheme, it is injective; in the case of an integral normal Noetherian scheme with a single isolated singularity, it distinguishes any two derived Brauer classes whose difference is of infinite order. As an application, we show that the canonical map is injective in the case of affine cones over smooth projective plane complex curves of degree greater than or equal to four as well as in the case of Mumford's (celebrated) singular surface.

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  1. Localizing motives of Azumaya algebras

    math.AG 2025-09 accept novelty 7.0 of 10

    The map Br^der(X) -> Pic(Mot_X) is injective for every qcqs scheme X.

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