Title: Extended Picard complexes and linear algebraic groups
Authors: Borovoi, Mikhail ×
van Hamel, Joost #
Issue Date: Feb-2009
Publisher: W. de Gruyter
Series Title: Journal für die Reine und Angewandte Mathematik (Crelle's Journal) vol:627 pages:53-82
Abstract: For a smooth geometrically integral variety X over a field k of characteristic 0, we introduce and investigate the extended Picard complex UPic(X). It is a certain complex of Galois modules of length 2, whose zeroth cohomology is (k) over bar [X](x)/(k) over bar (x) and whose first cohomology is Pic((X) over bar), where (k) over bar is a fixed algebraic closure of k and X is obtained from X by extension of scalars to (k) over bar. When X is a k-torsor of a connected linear k-group G, we compute UPic(X) = UPic(G) (in the derived category) in terms of the algebraic fundamental group pi(1)(G). As an application we compute the elementary obstruction for such X.
ISSN: 0075-4102
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

Files in This Item:

There are no files associated with this item.

Request a copy


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science