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Proceedings of the London Mathematical Society Advance Access published online on April 5, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn005
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© 2008 London Mathematical Society

Cohomology of bifunctors

Vincent Franjou

Laboratoire Jean Leray
Université de Nantes
BP 92208
44322 Nantes cedex 3
France

Eric M. Friedlander

Department of Mathematics
Northwestern University
Evanston, IL 60208
USA
eric@math.northwestern.edu

Received 28 March 2006. Revision received 23 May 2007.

We initiate the study of the cohomology of (strict polynomial) bifunctors by introducing the foundational formalism, establishing numerous properties in analogy with the cohomology of functors, and providing computational techniques. Since one of the initial motivations for the study of functor cohomology was the determination of H *(GL (k), S*(g{ell}) {otimes} {Lambda}*(g{ell})), we keep this challenging example in mind as we achieve numerous computations which illustrate our methods.

2000 Mathematics Subject Classification 20J06, 18G40.

The first author is partially supported by the LMJL – Laboratoire de Mathématiques Jean Leray, CNRS: Université de Nantes, École Centrale de Nantes. The second author is partially supported by the NSF.


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