**
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 9-26 (2002)
**

#
Picard Groups of Deligne-Lusztig Varieties - with a View toward Higher Codimensions

##
Soren Have Hansen

Centre for Mathematical Physics and Stochastics, Department of Mathematical Sciences, University of Aarhus, DK-8000 Aarhus C, Denmark, e-mail: shave@imf.au.dk

**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

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2002 ELibM for
the EMIS Electronic Edition
*