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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cotensor products of modules
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by L. Abrams and C. Weibel PDF
Trans. Amer. Math. Soc. 354 (2002), 2173-2185 Request permission

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
  • MR Author ID: 181325
  • Email: weibel@math.rutgers.edu
  • 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.
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 2173-2185
  • MSC (2000): Primary 16E30; Secondary 16W30, 16E40
  • DOI: https://doi.org/10.1090/S0002-9947-02-02883-0
  • MathSciNet review: 1885648