On a theorem of Hazrat and Hoobler
HTML articles powered by AMS MathViewer
- by Benjamin Antieau PDF
- Proc. Amer. Math. Soc. 141 (2013), 2609-2613 Request permission
Abstract:
We use cycle complexes with coefficients in an Azumaya algebra, as developed by Kahn and Levine, to compare the $G$-theory of an Azumaya algebra to the $G$-theory of the base scheme. We obtain a sharper version of a theorem of Hazrat and Hoobler in certain cases.References
- Benjamin Antieau, Cohomological obstruction theory for Brauer classes and the period-index problem, J. K-Theory 8 (2011), no. 3, 419–435. MR 2863419, DOI 10.1017/is010011030jkt136
- G. Cortiñas and C. Weibel, Homology of Azumaya algebras, Proc. Amer. Math. Soc. 121 (1994), no. 1, 53–55. MR 1181159, DOI 10.1090/S0002-9939-1994-1181159-5
- William G. Dwyer and Eric M. Friedlander, Étale $K$-theory of Azumaya algebras, Proceedings of the Luminy conference on algebraic $K$-theory (Luminy, 1983), 1984, pp. 179–191. MR 772057, DOI 10.1016/0022-4049(84)90035-5
- Thomas Geisser, Motivic cohomology over Dedekind rings, Math. Z. 248 (2004), no. 4, 773–794. MR 2103541, DOI 10.1007/s00209-004-0680-x
- S. Green, D. Handelman, and P. Roberts, $K$-theory of finite dimensional division algebras, J. Pure Appl. Algebra 12 (1978), no. 2, 153–158. MR 480698, DOI 10.1016/0022-4049(78)90030-0
- Alexander Grothendieck, Le groupe de Brauer. I. Algèbres d’Azumaya et interprétations diverses, Dix exposés sur la cohomologie des schémas, Adv. Stud. Pure Math., vol. 3, North-Holland, Amsterdam, 1968, pp. 46–66 (French). MR 244269
- R. Hazrat, Reduced $K$-theory of Azumaya algebras, J. Algebra 305 (2006), no. 2, 687–703. MR 2266848, DOI 10.1016/j.jalgebra.2006.01.038
- R. Hazrat and R. Hoobler, K-theory of Azumaya algebras over schemes, arXiv e-prints (2009), 0911.1406. To appear in Communications in Algebra.
- Roozbeh Hazrat and Judith R. Millar, A note on $K$-theory of Azumaya algebras, Comm. Algebra 38 (2010), no. 3, 919–926. MR 2650377, DOI 10.1080/00927870902828710
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- Bruno Kahn and Marc Levine, Motives of Azumaya algebras, J. Inst. Math. Jussieu 9 (2010), no. 3, 481–599. MR 2650808, DOI 10.1017/S1474748010000022
- R. W. Thomason, Algebraic $K$-theory and étale cohomology, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 3, 437–552. MR 826102
Additional Information
- Benjamin Antieau
- Affiliation: Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
- MR Author ID: 924946
- Email: antieau@math.ucla.edu
- Received by editor(s): April 4, 2011
- Received by editor(s) in revised form: November 7, 2011
- Published electronically: April 19, 2013
- Additional Notes: The author was supported in part by the NSF under Grant RTG DMS 0838697
- Communicated by: Lev Borisov
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2609-2613
- MSC (2010): Primary 14F22; Secondary 19Dxx
- DOI: https://doi.org/10.1090/S0002-9939-2013-11656-4
- MathSciNet review: 3056551