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

 

Cotensor products of modules


Authors: L. Abrams and C. Weibel
Journal: Trans. Amer. Math. Soc. 354 (2002), 2173-2185
MSC (2000): Primary 16E30; Secondary 16W30, 16E40
Published electronically: February 1, 2002
MathSciNet review: 1885648
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Abstract: Let $C$ be a coalgebra over a field $k$ and $A$ its dual algebra. The category of $C$-comodules is equivalent to a category of $A$-modules. We use this to interpret the cotensor product $M \square N$ of two comodules in terms of the appropriate Hochschild cohomology of the $A$-bimodule $M \otimes N$, when $A$ is finite-dimensional, profinite, graded or differential-graded. The main applications are to Galois cohomology, comodules over the Steenrod algebra, and the homology of induced fibrations.


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Additional Information

L. Abrams
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication: Department of Mathematics, George Washington University, Washington, D.C. 20052
Email: labrams@gwu.edu

C. Weibel
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: weibel@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02883-0
PII: S 0002-9947(02)02883-0
Received by editor(s): April 18, 2000
Received by editor(s) in revised form: June 14, 2001
Published electronically: February 1, 2002
Additional Notes: The second author was partially supported by NSF grants.
Article copyright: © Copyright 2002 American Mathematical Society