TY - JOUR

T1 - Extended Picard complexes for algebraic groups and homogeneous spaces

AU - Borovoi, Mikhail

AU - van Hamel, Joost

N1 - Funding Information:
E-mail addresses: borovoi@post.tau.ac.il (M. Borovoi), Joost.vanHamel@wis.kuleuven.ac.be (J. van Hamel). 1 Partially supported by the Hermann Minkowski Center for Geometry.

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=33645956544&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2006.02.030

DO - 10.1016/j.crma.2006.02.030

M3 - מאמר

AN - SCOPUS:33645956544

VL - 342

SP - 671

EP - 674

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 9

ER -