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

 

Deformations of schemes and other bialgebraic structures


Author: J. P. Pridham
Journal: Trans. Amer. Math. Soc. 360 (2008), 1601-1629
MSC (2000): Primary 14B12, 14D15, 13D10
Published electronically: July 23, 2007
MathSciNet review: 2357707
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Abstract: There has long been a philosophy that every deformation problem in characteristic zero should be governed by a differential graded Lie algebra (DGLA). In this paper, we show how to construct a Simplicial Deformation Complex (SDC) governing any bialgebraic deformation problem. Examples of such problems are deformations of a Hopf algebra, or of an arbitrary scheme. In characteristic zero, SDCs and DGLAs are shown to be equivalent.


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Additional Information

J. P. Pridham
Affiliation: Trinity College, Cambridge, CB2 1TQ, United Kingdom
Email: J.P.Pridham@dpmms.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04355-3
PII: S 0002-9947(07)04355-3
Received by editor(s): October 31, 2005
Received by editor(s) in revised form: April 25, 2006
Published electronically: July 23, 2007
Additional Notes: The author was supported during this research by Trinity College, Cambridge and by the Isle of Man Department of Education
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.