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On the motive of the group of units of a division algebra

Published online by Cambridge University Press:  17 March 2014

Evgeny Shinder
Evgeny Shinder*
Affiliation:
Edinburgh Hodge Institute, The University of Edinburgh, School of Mathematics, The King's Buildings, Edinburgh EH6 3JL, [email protected]
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Abstract

We consider the algebraic group GL1 (A), where A is a division algebra of prime degree over a field F, and the associated motive in the Voevodsky category of motivic complexes (F). We relate the motive of GL1 (A) to the motive of the Čech simplicial scheme χ, associated to the Severi-Brauer variety of A, and compute the second differential in the resulting spectral sequence for motivic cohomology.

Keywords

division algebraSeveri-Brauer varietymotivic cohomology17A3511E5714F4219E15
Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 3 , June 2014 , pp. 533 - 561
Copyright
Copyright © ISOPP 2014 

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