### Abstract

Original language | English |
---|---|

Pages (from-to) | 1268-1277 |

Journal | Communications in Algebra |

Volume | 41 |

Issue number | 4 |

DOIs | |

Publication status | Published - 02 Apr 2013 |

### Fingerprint

### Cite this

*Communications in Algebra*,

*41*(4), 1268-1277. https://doi.org/10.1080/00927872.2011.608764

}

*Communications in Algebra*, vol. 41, no. 4, pp. 1268-1277. https://doi.org/10.1080/00927872.2011.608764

**K-Theory of Azumaya Algebras over Schemes.** / Hazrat, Roozbeh ; Hoobler, Raymond T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - K-Theory of Azumaya Algebras over Schemes

AU - Hazrat, Roozbeh

AU - Hoobler, Raymond T.

PY - 2013/4/2

Y1 - 2013/4/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84875931670&partnerID=8YFLogxK

U2 - 10.1080/00927872.2011.608764

DO - 10.1080/00927872.2011.608764

M3 - Article

AN - SCOPUS:84875931670

VL - 41

SP - 1268

EP - 1277

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -