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arXiv · 1408.1581

Equivariant Anderson duality and Mackey functor duality

Nicolas Ricka
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Abstract

We show that the $\mathbb{Z}/2$-equivariant Morava K-theories with reality (as defined by Hu) are self-dual with respect to equivariant Anderson duality. In particular, there is a universal coefficients exact sequence in Morava K-theory with reality. As a particular example, we recover the self-duality of the spectrum $KO$. The study of $\mathbb{Z}/2$-equivariant Anderson duality made in this paper gives a nice interpretation of some symmetries of $RO(\mathbb{Z}/2)$-graded (i.e. bigraded) equivariant cohomology groups in terms of Mackey functor duality.

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Nicolas Ricka. 2014-08-07. Equivariant Anderson duality and Mackey functor duality. https://doi.org/10.1017/s0017089515000397

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