Extended Picard complexes for algebraic groups and homogeneous spaces

Mikhail Borovoi, Joost van Hamel

Research output: Contribution to journalArticlepeer-review

Abstract

For a smooth geometrically integral algebraic variety X over a field k of characteristic 0, we define the extended Picard complex UPic ( over(X, ̄) ). It is a complex of length 2 which combines the Picard group Pic ( over(X, ̄) ) and the group U ( over(X, ̄) ) : = over(k, ̄) [ over(X, ̄) ]× / over(k, ̄)×, where over(k, ̄) is a fixed algebraic closure of k and over(X, ̄) = X ×k over(k, ̄). For a connected linear k-group G we compute the complex UPic ( over(G, ̄) ) (up to a quasi-isomorphism) in terms of the algebraic fundamental group π1 ( over(G, ̄) ). We obtain similar results for a homogeneous space X of a connected k-group G. To cite this article: M. Borovoi, J. van Hamel, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Original languageEnglish
Pages (from-to)671-674
Number of pages4
JournalComptes Rendus Mathematique
Volume342
Issue number9
DOIs
StatePublished - 1 May 2006

Fingerprint

Dive into the research topics of 'Extended Picard complexes for algebraic groups and homogeneous spaces'. Together they form a unique fingerprint.

Cite this