Upper motives of products of projective linear groups

Charles De Clercq

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arXiv · 1110.0391

Upper motives of products of projective linear groups

Charles De Clercq

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Abstract

Fix a base field F, a finite field K and consider a sequence of central simple F-algebras A_1,...,A_n. In this note we provide some results toward a classification of the indecomposable motives lying in the motivic decompositions of projective homogeneous varieties under the action of PGL(A_1)x...xPGL(A_n) with coefficients in K. We give a complete classification of those motives if n=1 and derive from it the motivic dichotomy of projective linear groups. We then provide several classification results as well as counterexamples for arbitrary n showing that the situation is less rigid. These results involve a neat study of rational maps between generalized Severi-Brauer varieties which is certainly of independent interest.

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BibTeX RIS

Charles De Clercq. 2011-12-21. Upper motives of products of projective linear groups. https://arxiv.org/abs/1110.0391

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