Motivic rigidity of Severi-Brauer varieties

Details Motivic rigidity of Severi-Brauer varieties Motivic rigidity of Severi-Brauer varieties

2011-05-25

arxiv.org/abs/1105.4981v2

Mathematics

Algebraic Geometry

v2, more details added

Scientific paper

Let D be a division algebra over a field F. We study in this note the rigidity of the motivic decompositions of the Severi-Brauer varieties of D, with respect to the ring of coefficients and to the base field. We first show that these decompositions only depend on the characteristic of the field of coefficients. In a second part we show that if D remains division over a field extension E/F, the motivic decompositions of several Severi-Brauer varieties of D lift to E.

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