Invertible modules for commutative S-algebras with residue fields

Baker, A. and Richter, B. (2005) Invertible modules for commutative S-algebras with residue fields. Manuscripta Mathematica, 118(1), pp. 99-119. (doi: 10.1007/s00229-005-0582-1)

Full text not currently available from Enlighten.

Publisher's URL:


The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules over the coefficient ring by taking homotopy groups. If a connective commutative S-algebra R has coherent localizations (R*)m for every maximal ideal m◄R*, then for every invertible R-module U, U*=π*U is an invertible graded R*-module. In some non-connective cases we can carry the result over under the additional assumption that the commutative S-algebra has ‘residue fields’ for all maximal ideals m◄R* if the global dimension of R* is small or if R is 2-periodic with underlying Noetherian complete local regular ring R0. We apply these results to finite abelian Galois extensions of Lubin-Tate spectra.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A., and Richter, B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Manuscripta Mathematica
ISSN (Online):1432-1785
Published Online:10 August 2005

University Staff: Request a correction | Enlighten Editors: Update this record