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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexI gave _[[chromatic homotopy theory]]_ an Idea-section. To be expanded eventually...

   I gave chromatic homotopy theory an Idea-section.

   To be expanded eventually…

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeApr 16th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI added the reference * Tobias Barthel, Tomer Schlank, Nathaniel Stapleton, _Chromatic homotopy theory is asymptotically algebraic_, ([arXiv:1711.00844](https://arxiv.org/abs/1711.00844)) <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/35">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/35">v35</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   I added the reference

   • Tobias Barthel, Tomer Schlank, Nathaniel Stapleton, Chromatic homotopy theory is asymptotically algebraic, (arXiv:1711.00844)

   diff, v35, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 14th 2018
   • (edited Jun 14th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointers to [Heuts 18](https://ncatlab.org/nlab/show/chromatic+homotopy+theory#Heuts18) and [Lurie-Hopkins 18](https://ncatlab.org/nlab/show/chromatic+homotopy+theory#LurieHopkins18) (on the unstable case) <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/37">v37</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   added pointers to Heuts 18 and Lurie-Hopkins 18 (on the unstable case)

   diff, v37, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 9th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Aldridge Bousfield]], _Localization and periodicity in unstable homotopy theory_, J. Amer. Math. Soc. 7 (1994), 831-873 ([doi:10.1090/S0894-0347-1994-1257059-7](https://doi.org/10.1090/S0894-0347-1994-1257059-7), [jstor:2152734](https://www.jstor.org/stable/2152734)) <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/38">v38</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   added pointer to:

   • Aldridge Bousfield, Localization and periodicity in unstable homotopy theory, J. Amer. Math. Soc. 7 (1994), 831-873 (doi:10.1090/S0894-0347-1994-1257059-7, jstor:2152734)

   diff, v38, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 9th 2020
   • (edited Sep 9th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItex[ duplicate deleted ]

   [ duplicate deleted ]

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 9th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data to the original article: * [[Mark Mahowald]], [[Doug Ravenel]], _Towards a Global Understanding of the Homotopy Groups of Spheres_, pages 57-74 in Part II of: _The Lefschetz Centennial Conference -- Proceedings on Algebraic Topology_, Proceedings of the Lefschetz Centennial Conference held December 10-14, 1984, Contemporary Mathematics 58, American Mathematical Society, 1987. ([ISBN:978-0-8218-5063-3](https://bookstore.ams.org/conm-58-2), [pdf](http://www.math.rochester.edu/people/faculty/doug/mypapers/global.pdf), [[MahowaldRavenelHomotopyGroupsOfSpheres.pdf:file]]) <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/38">v38</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   added publication data to the original article:

   • Mark Mahowald, Doug Ravenel, Towards a Global Understanding of the Homotopy Groups of Spheres, pages 57-74 in Part II of: The Lefschetz Centennial Conference – Proceedings on Algebraic Topology, Proceedings of the Lefschetz Centennial Conference held December 10-14, 1984, Contemporary Mathematics 58, American Mathematical Society, 1987. (ISBN:978-0-8218-5063-3, pdf, MahowaldRavenelHomotopyGroupsOfSpheres.pdf:file)

   diff, v38, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 16th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Tobias Barthel]], [[Agnès Beaudry]], *Chromatic structures in stable homotopy theory*, in [[Handbook of Homotopy Theory]], Chapman and Hall/CRC Press (2019) &lbrack;[arXiv:1901.09004](https://arxiv.org/abs/1901.09004), [doi:10.1201/9781351251624](https://doi.org/10.1201/9781351251624)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/44">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/44">v44</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   added pointer to:

   • Tobias Barthel, Agnès Beaudry, Chromatic structures in stable homotopy theory, in Handbook of Homotopy Theory, Chapman and Hall/CRC Press (2019) [arXiv:1901.09004, doi:10.1201/9781351251624]

   diff, v44, current

8. • CommentRowNumber8.
   • CommentAuthorZaslav
   • CommentTimeJan 14th 2024
   • PermaLink
   Author: Zaslav
   Format: MarkdownItexRm self-link [[chromatic filtration]]. <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/46">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/46">v46</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

   Rm self-link chromatic filtration.

   diff, v46, current

9. • CommentRowNumber9.
   • CommentAuthorZaslav
   • CommentTimeJan 14th 2024
   • PermaLink
   Author: Zaslav
   Format: TextWhat is chromatic about this theory? The name is a puzzle.

   What is chromatic about this theory? The name is a puzzle.
10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2024
    • (edited Jan 14th 2024)
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded, to the beginning of the Idea-section, this quote from [Ravenel 1992, p. 24](https://ncatlab.org/nlab/show/chromatic+homotopy+theory#Ravenel92): > We use the word 'chromatic' here for the following reason. The $n$-th subquotients in the chromatic filtration consists of $v_n$-periodic elements. As illustrated in 2.4.2, these elements fall into periodic families. The chromatic filtration is thus like a spectrum in the astronomical sense in that it resolves the stable homotopy groups of a finite complex into periodic families of various periods. Comparing these to the colors of the rainbow led us to the word 'chromatic'. <a href="https://ncatlab.org/nlab/revision/diff/chromatic+homotopy+theory/47">diff</a>, <a href="https://ncatlab.org/nlab/revision/chromatic+homotopy+theory/47">v47</a>, <a href="https://ncatlab.org/nlab/show/chromatic+homotopy+theory">current</a>

    added, to the beginning of the Idea-section, this quote from Ravenel 1992, p. 24:

    We use the word ’chromatic’ here for the following reason. The $n$-th subquotients in the chromatic filtration consists of $v_n$-periodic elements. As illustrated in 2.4.2, these elements fall into periodic families. The chromatic filtration is thus like a spectrum in the astronomical sense in that it resolves the stable homotopy groups of a finite complex into periodic families of various periods. Comparing these to the colors of the rainbow led us to the word ’chromatic’.

    diff, v47, current