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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Change of rings in deformation theory of modules


Author: Runar Ile
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 4873-4896
MSC (2000): Primary 13D10, 14B10; Secondary 13D07
Published electronically: January 29, 2004
MathSciNet review: 2084403
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Abstract: Given a $B$-module $ M $ and any presentation $ B=A/J $, the obstruction theory of $ M $ as a $ B $-module is determined by the usual obstruction class $ \mathrm{o}_{ \scriptscriptstyle{A}}^{\scriptscriptstyle{}}$ for deforming $ M $ as an $ A $-module and a new obstruction class $ \mathrm{o}_{ \scriptscriptstyle{J}}^{\scriptscriptstyle{}} $. These two classes give the tool for constructing two obstruction maps which depend on each other and which characterise the hull of the deformation functor. We obtain relations between the obstruction classes by studying a change of rings spectral sequence and by representing certain classes as elements in the Yoneda complex. Calculation of the deformation functor of $ M $ as a $ B $-module, including the (generalised) Massey products, is thus possible within any $ A $-free $ 2 $-presentation of $ M $.


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Additional Information

Runar Ile
Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway
Email: ile@math.uio.no

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03516-0
PII: S 0002-9947(04)03516-0
Keywords: Obstruction, Massey product, spectral sequence, mixed characteristic
Received by editor(s): April 20, 2003
Published electronically: January 29, 2004
Additional Notes: This article is based on parts of the author’s 2001 Ph.D. Thesis at the Department of Mathematics, University of Oslo.
Article copyright: © Copyright 2004 American Mathematical Society