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Proceedings of the American Mathematical Society

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Obstructions to deformations of d.g. modules


Authors: Trina Armstrong and Ron Umble
Journal: Proc. Amer. Math. Soc. 129 (2001), 3447-3452
MSC (2000): Primary 13D10
DOI: https://doi.org/10.1090/S0002-9939-01-06293-1
Published electronically: July 2, 2001
MathSciNet review: 1860475
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Abstract:

Let $\mathbf{k}$ be a field and $n\geq1$. There exist a differential graded $\mathbf{k}$-module $(V,d)$ and various approximations to a differential $d+td_{1}+t^{2}d_{2}+\cdots+ t^{n}d_{n}$ on $V[[t]],$ one of which gives a non-trivial deformation, another is obstructed, and another is unobstructed at order $n$. The analogous problem in the category of $\mathbf{k}$-algebras in characteristic zero remains a long-standing open question.


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Additional Information

Trina Armstrong
Affiliation: Department of Health Evaluation Sciences, Penn State College of Medicine, MC H173, P.O. Box 850, 500 University Dr., Hershey, Pennsylvania 17033
Email: tja3@psu.edu

Ron Umble
Affiliation: Department of Mathematics, Millersville University of Pennsylvania, Millersville, Pennsylvania 17551
Email: Ron.Umble@millersville.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06293-1
Received by editor(s): February 9, 1995
Published electronically: July 2, 2001
Additional Notes: This paper reports the results of an undergraduate honors project directed by the second author.
Communicated by: Eric Friedlander
Article copyright: © Copyright 2001 American Mathematical Society