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

摘要

We consider the algebraic group GL_1 (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 DM_~(eff) (F). We relate the motive of GL_1 (A) to the motive of the ?ech simplicial scheme X, associated to the Severi-Brauer variety of A, and compute the second differential in the resulting spectral sequence for motivic cohomology.