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Hopf-theoretic approach to motives of twisted flag varieties

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arxiv 1908.08770 v2 pith:5OCPMD5F submitted 2019-08-23 math.AG

classification math.AG
keywords approachmotivesvarietiesflagstructuretwistedalgebraalgebraic
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abstract

Let $G$ be a split semisimple algebraic group over a field and let $A^*$ be an oriented cohomology theory in the sense of Levine--Morel. We provide a uniform approach to the $A^*$-motives of geometrically cellular smooth projective $G$-varieties based on the Hopf algebra structure of $A^*(G)$. Using this approach we provide various applications to the structure of motives of twisted flag varieties.

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