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severi-brauer variety

Journal of K-Theory (1)

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On the motive of the group of units of a division algebra
Evgeny Shinder
Journal:

Journal of K-Theory / Volume 13 / Issue 3 / June 2014

Published online by Cambridge University Press:

17 March 2014, pp. 533-561

Print publication:

June 2014
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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.