Journal of the Ramanujan Mathematical Society

Volume 28, Issue 2, June 2013 pp. 159–172.

Upper motives of products of projective linear groups

Authors: Charles De Clercq
Author institution: Université Paris VI, 4 place Jussieu, 75252 Paris CEDEX 5

Summary: This paper is devoted to the classification of the upper motives of all the products of projective linear groups with coefficients in a finite field. We~first give a complete classification of the upper motives of all the projective linear groups and derive from it the motivic dichotomy. We then provide several classification results as well as counterexamples for arbitrary products of projective linear groups, showing that the situation is less rigid. The proofs involve a neat study of rational maps between generalized Severi-Brauer varieties which is certainly of independent interest.

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