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Constructing the determinant sphere using a Tate twist. (arXiv:1810.06651v1 [math.AT])
来源于:arXiv
Following an idea of Hopkins, we construct a model of the determinant sphere
$S\langle det \rangle$ in the category of $K(n)$-local spectra. To do this, we
build a spectrum which we call the Tate sphere $S(1)$. This is a $p$-complete
sphere with a natural continuous action of $\mathbb{Z}_p^\times$. The Tate
sphere inherits an action of $\mathbb{G}_n$ via the determinant and smashing
Morava $E$-theory with $S(1)$ has the effect of twisting the action of
$\mathbb{G}_n$. A large part of this paper consists of analyzing continuous
$\mathbb{G}_n$-actions and their homotopy fixed points in the setup of Devinatz
and Hopkins. 查看全文>>