Year: 2010
Type: preprint
Abstract: Let k be a field of characteristic 0 and let X be a smooth geometrically integral k-variety. In our previous paper we defined the extended Picard complex UPic(X) as a certain complex of Galois modules in degrees 0 and 1. We computed the isomorphism class of UPic(G) in the derived category of Galois modules for a connected linear k-group G. In this paper we assume that X is a homogeneous space of a connected linear k-group G with geometric stabilizer H. We compute the isomorphism class of UPic(X) in the derived category of Galois modules in terms of the character groups of G and H. The proof is based on the notion of the extended equivariant Picard complex UPic_G(X) of a G-variety X.
Source: arXiv (Cornell University)
Authors: Borovoi, Mikhail, van Hamel, Joost
Institutions: Tel Aviv University, KU Leuven
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950331624