Timeline for Detecting the Brown-Comenetz dualizing spectrum

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Jun 8, 2018 at 17:45	history	edited	Neil Strickland	CC BY-SA 4.0	added 805 characters in body
Jun 4, 2018 at 2:30	comment	added	skd		Regarding the last paragraph: there is a trigraded spectral sequence converging to $\mathrm{Ext}^{s+n,t}(BP_\ast F(\infty), BP_\ast)$ whose $E_2$-page is $\varprojlim^n \mathrm{Ext}^{s,t}(BP_\ast F(m), BP_\ast)$. I don't know if it's any easier to show that these groups vanish.
Jun 4, 2018 at 2:27	comment	added	skd		Thanks! Just want to point out one other way to show that $L^f_n I = 0$. Since $L^f_n$-localization is smashing and $\langle L^f_n S \rangle \leq \langle T(0) \vee \cdots \vee T(n)\rangle$, it suffices to show that $T(n) \wedge I = 0$ for all $n$. As $\langle \mathbf{F}_p\rangle \geq \langle I\rangle$ (since the homotopy groups of $I$ are bounded above and torsion), it suffices to show that $T(n)\wedge \mathbf{F}_p = 0$. For $n=0$ this is obvious, and for $n>0$ this follows since $v_n$-self maps have positive Adams filtration.
Jun 3, 2018 at 22:39	history	answered	Neil Strickland	CC BY-SA 4.0