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On the classification of unstable $H^{\ast}V-A$-modules

Dorra Bourguiba

In this work, we begin studying the classification, up to isomorphism, of unstable $\mathrm{H}^{\ast}V-A$-modules $E$ such that $\mathbb{F}_{2} \otimes _{\mathrm{H}^{\ast}V} E $ is isomorphic to a given unstable $A$-module $M$. In fact this classification depends on the structure of $M$ as unstable $A$-module. In this paper, we are interested in the case $M$ a nil-closed unstable $A$-module and the case $M$ is isomorphic to $\sum^{n}\mathbb{F}_{2}$. We also study, for $V=\mathbb{Z}/2\mathbb{Z}$, the case $M$ is the Brown-Gitler module $\mathrm{J}(2)$.

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 69-82