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Motivic decomposition of certain special linear groups


Author: Alexander S. Merkurjev
Journal: Trans. Amer. Math. Soc. 369 (2017), 555-574
MSC (2010): Primary 20G15; Secondary 19E15, 14F42
DOI: https://doi.org/10.1090/tran6654
Published electronically: March 21, 2016
MathSciNet review: 3557785
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Abstract: We compute the motive of the algebraic group $ G=\operatorname {\mathbf {SL}}_1(D)$ for a central simple algebra $ D$ of prime degree over a perfect field. As an application we determine certain motivic cohomology groups and differentials in the motivic spectral sequence of $ G$.


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Additional Information

Alexander S. Merkurjev
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Email: merkurev@math.ucla.edu

DOI: https://doi.org/10.1090/tran6654
Keywords: Central simple algebras, Severi-Brauer varieties, special linear groups, motives, motivic cohomology
Received by editor(s): March 13, 2014
Received by editor(s) in revised form: January 10, 2015
Published electronically: March 21, 2016
Additional Notes: The work of the author has been supported by NSF grant DMS #1160206 and a Guggenheim Fellowship
Article copyright: © Copyright 2016 American Mathematical Society

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