K-Theory of Azumaya Algebras over Schemes

Roozbeh Hazrat, Raymond T. Hoobler

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let X be a connected, noetherian scheme and A{script} be a sheaf of Azumaya algebras on X, which is a locally free O{script}-module of rank a. We show that the kernel and cokernel of K(X) ? K(A{script}) are torsion groups with exponent a for some m and any i = 0, when X is regular or X is of dimension d with an ample sheaf (in this case m = d + 1). As a consequence, K(X, Z/m) ? K(A{script}, Z/m), for any m relatively prime to a.
Original languageEnglish
Pages (from-to)1268-1277
JournalCommunications in Algebra
Volume41
Issue number4
DOIs
Publication statusPublished - 02 Apr 2013

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