2016
DOI: 10.1515/crelle-2016-0015
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Motivic decomposition of compactifications of certain group varieties

Abstract: Abstract Let D be a central simple algebra of prime degree over a field and let E be an {\operatorname{\mathbf{SL}}_{1}(D)} Show more

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Cited by 2 publications
(2 citation statements)
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“…In particular, R F (X) is split and Ch 0 R = Ch 0 R F (X) = F is non-zero. Note that the structure of the total motive of X is a complete mystery and is understood only in very special situations (namely, when p = 2 and X is a projective quadric; when n = 1 and X is a Severi-Brauer variety; and finally, when n = 2 and X is a smooth equivariant compactification of the special linear group of a central division algebra of prime degree, [11]).…”
Section: Remarkmentioning
confidence: 99%
“…In particular, R F (X) is split and Ch 0 R = Ch 0 R F (X) = F is non-zero. Note that the structure of the total motive of X is a complete mystery and is understood only in very special situations (namely, when p = 2 and X is a projective quadric; when n = 1 and X is a Severi-Brauer variety; and finally, when n = 2 and X is a smooth equivariant compactification of the special linear group of a central division algebra of prime degree, [11]).…”
Section: Remarkmentioning
confidence: 99%
“…In other words, X is a projective variety equipped with an action of G × G and containing G as an open orbit on which the group G × G acts by the left-right translations. The motive of X is split (i.e., M(X) is a direct sum of Tate motives) over any field extension that splits D by [10,Theorem 6.5].…”
Section: Compactifications Of Gmentioning
confidence: 99%