Title: Extended Picard complexes for algebraic groups and homogeneous spaces
Authors: Borovoi, M ×
van Hamel, Joost #
Issue Date: 2006
Publisher: Elsevier france-editions scientifiques medicales elsevier
Series Title: Comptes rendus mathematique vol:342 issue:9 pages:671-674
Abstract: For a smooth geometrically integral algebraic variety X over a field k of characteristic 0, we define the extended Picard complex where (k) over bar is UPic((X) over bar). It is a complex of length 2 which combines the Picard group Pic((X) over bar) and the group U((X) over bar) := (k) over bar[(K) over bar](x)/(k) over bar (x) where (k) over bar is a fixed algebraic closure of k and (X) over bar = X x(k) (k) over bar. For a connected linear k-group G we compute the complex UPic((G) over bar) (up to a quasi-isomorphism) in terms of the algebraic fundamental group pi(1) ((G) over bar). We obtain similar results for a homogeneous space X of a connected k-group G.
ISSN: 1631-073X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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