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Extended equivariant Picard complexes and homogeneous spaces

Authors:

Institution:

1. Raymond and Beverly Sackler, School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel
2. K. U. Leuven, Departement Wiskunde, Celestijnenlaan 200B, B-3001, Leuven (Heverlee), Belgium

Abstract:

Let k be a field of characteristic 0 and let `(k)] \bar{k} be a fixed algebraic closure of k. Let X be a smooth geometrically integral k-variety; we set `(X)] = X ×_k`(k)] \bar{X} = X{ \times_k}\bar{k} and denote by `(X)] \bar{X} . In BvH2] we defined the extended Picard complex of X as the complex of Gal( `(k)]

k ) Gal\left( {{{{\bar{k}}} \left/ {k} \right.}} \right) -modules

\textDiv( `(X)] ) {\text{Div}}\left( {\bar{X}} \right) is in degree 1. We computed the isomorphism class of \textUPic( `(G)] ) {\text{UPic}}\left( {\bar{G}} \right) in the derived category of Galois modules for a connected linear k-group G.

Keywords:
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