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Drew Heard's user avatar
Drew Heard's user avatar
Drew Heard
  • Member for 13 years, 4 months
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Detecting the Brown-Comenetz dualizing spectrum
I just noticed your comments to the question - it seems you have already noticed that (1) is equivalent to (3)!
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Realizing the 0-th Postnikov truncation of a spectrum in the category of orthogonal/symmetric spectra
Doesn't remark II.8.2 of Schwede's book suggest that the answer is yes?
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Finding decomposition of Steenrod operators?
Such decompositions are not unique, as (for example) $Sq^6 = Sq^2Sq^4 + Sq^1Sq^2Sq^1Sq^2$ as well. Sage can do these types of change of basis for you. But you might also find what you want in mathweb.scranton.edu/monks/pubs/bases.pdf (Look at Wall's basis and Arnon's A basis)
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How to think about $\mathbf{Z}(n)_{\mathcal{M}}$
The result on Betti realization that you want is proved in Section 4 of Heller--Ormsby (arxiv.org/pdf/1401.4728.pdf)
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What is $Ext^1 (M\otimes_R N,L)$?
There should be more extensions in Ext^1 - it's equivalence classes of extensions of M by N. e.g., 0 --> Z/2 ---> Z/4 ---> Z/2 --> 0 corresponds to the non-zero element of Ext^1(Z/2,Z/2)
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What is $Ext^1 (M\otimes_R N,L)$?
Indeed, Section 5 of the cited paper tells you that Ext^n_R(M,N) = Ch(R)(P_,S^n(N))\~, where P_ is a projective resolution of M
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What is $Ext^1 (M\otimes_R N,L)$?
When using Lemma 2.1, aren't you making the assumption that (i) Ext_{dw}^1(X,\Sigma^{-n-1}Y) = \Ext_{dw}^n(X,Y) (for whatever the latter means, since it is not defined in the cited paper) (ii) That Ext_{dw}^n(M,N) = \Ext_R^n(M,N).
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What is the symmetric monoidal structure on the $(\infty,1)$-category of spectra?
Shouldn't $\partial_1$ be right adjoint to the inclusion?
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References for computation of 2-primary stable 64-stem ${_2\pi_{64}^s}$?
@user51223 See the bottom of page 4 of arxiv.org/pdf/1407.8418.pdf - there are some inconsistencies with the latest calculations and the Kochman/Mahowald calculations. Thus, I'm not sure if the calculation in the 64 stem is correct.
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Strong Convergence vs Conditional Convergence for Spectral Sequences (Is there a simple explanation?)
The usual reference for these types of things is Boardman's 'Conditionally convergent spectral sequences' - citeseerx.ist.psu.edu/viewdoc/…. The remark after Theorem 7.1 suggests the answer to your question is that such a spectral sequence strongly converges.
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$C_2$-equivariant Betti realization of MGL
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