Margolis homology

General Introduction
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Search results
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Online References
Voevodsky: Motivic cohomology with Z/2 coeffs. Mentions the motivic analogue of Margolis homology, and some background on the topological version. See pp 14.
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
List mail from Andrew Salch:
Let k be a finite field of characteristic p and let A be a cocommutative Hopf algebra over k. For each primitive x in A satisfying x^p = 0, one has a pair of Margolis homology functors defined on the category of Amodules: H0(M, x) = (ker f)/(im f^{p1}) and H1(M, x) = (ker f^{p1})/(im f), where f is the selfmap of M given by multiplication by x. If p=2 then H0(M, x) coincides with H1(M, x).
Margolis, in his book "Spectra and the Steenrod algebra," proves that, if A is an exterior algebra or the Steenrod algebra (or a subHopfalgebra of it) at the prime 2, there is a Whitehead theorem for Margolis homology: if a map of boundedbelow Amodules induces an isomorphism in all of A's Margolis homology theories, then the map of Amodules has projective kernel and projective cokernel.
Is it known for what other cocommutative Hopf algebras A this analogue of Whitehead's theorem holds?
Thanks, Andrew S.
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