Transactions of the American Mathematical Society

Author(s): Runar Ile
Journal: Trans. Amer. Math. Soc. 356 (2004), 4873-4896.
MSC (2000): Primary 13D10, 14B10; Secondary 13D07
Posted: January 29, 2004
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Abstract: Given a

-module

and any presentation

, the obstruction theory of

as a

-module is determined by the usual obstruction class $\mathrm{o}_{ \scriptscriptstyle{A}}^{\scriptscriptstyle{}}$ for deforming

as an

-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

as a

-module, including the (generalised) Massey products, is thus possible within any

-free

-presentation of

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13D10, 14B10, 13D07

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

DOI: 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
Posted: 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.
Copyright of article: Copyright 2004, American Mathematical Society

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