Abstract: For a Deligne-Lusztig variety $\bar X (w)$ arising from one of the classical (possibly twisted) groups, we show that the Picard group of $\bar X(w)$ is generated by the finitely many Deligne-Lusztig subvarieties of $\bar X (w)$. It is conjectured that this more generally should hold in any codimension, and a good deal of supporting evidence for this claim is presented.
Keywords: algebraic geometry, algebraic groups, Deligne-Lusztig varieties, Picard (and Chow) groups
Classification (MSC2000): 14M15,14C25
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