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Ravenel's conjectures
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Homotopy_groups_of_spheres/YMENlGgd">Homotopy groups of spheres</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Ravenel, Douglas C. (1984). "Localization with Respect to Certain Periodic Homology Theories" (PDF). American Journal of Mathematics. 106 (2): 351–414. doi:10.2307/2374308. JSTOR 2374308. MR 0737778. <a href="https://www.math.rochester.edu/people/faculty/doug/mypapers/loc.pdf" target="_blank">https://www.math.rochester.edu/people/faculty/doug/mypapers/loc.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Hopkins, Michael J. (2008). "The mathematical work of Douglas C. Ravenel" (PDF). Homology, Homotopy and Applications. 10 (3, Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson): 1–13. doi:10.4310/HHA.2008.v10.n3.a1. <a href="http://www.intlpress.com/HHA/v10/n3/a1/v10n3a1.pdf" target="_blank">http://www.intlpress.com/HHA/v10/n3/a1/v10n3a1.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Devinatz, Ethan S.; Hopkins, Michael J.; Smith, Jeffrey H. (1988). "Nilpotence and stable homotopy theory. I". Annals of Mathematics. Second Series. 128 (2): 207–241. doi:10.2307/1971440. ISSN 0003-486X. JSTOR 1971440. MR 0960945. <a href="/wiki/Michael_J._Hopkins" target="_blank">/wiki/Michael_J._Hopkins</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Hopkins, Michael J.; Smith, Jeffrey H. (1998). "Nilpotence and Stable Homotopy Theory II". Annals of Mathematics. Second Series. 148 (1): 1–49. CiteSeerX 10.1.1.568.9148. doi:10.2307/120991. JSTOR 120991. <a href="/wiki/Michael_J._Hopkins" target="_blank">/wiki/Michael_J._Hopkins</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Hopkins, Michael J. (2008). "The mathematical work of Douglas C. Ravenel" (PDF). Homology, Homotopy and Applications. 10 (3, Proceedings of a Conference in Honor of Douglas C. Ravenel and W. Stephen Wilson): 1–13. doi:10.4310/HHA.2008.v10.n3.a1. <a href="http://www.intlpress.com/HHA/v10/n3/a1/v10n3a1.pdf" target="_blank">http://www.intlpress.com/HHA/v10/n3/a1/v10n3a1.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Brüning, Kristian (2007). Subcategories of Triangulated Categories and the Smashing Conjecture (PDF) (Thesis). Dissertation zur Erlangung des akademischen Grades. p. 25. <a href="https://pace.uni-paderborn.de/fileadmin/pace/IRTG/PhD_Thesis/k1_m60.pdf" target="_blank">https://pace.uni-paderborn.de/fileadmin/pace/IRTG/PhD_Thesis/k1_m60.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Jack, Hall; David, Rydh (2016-06-27). "The telescope conjecture for algebraic stacks". Journal of Topology. 10 (3): 776–794. arXiv:1606.08413. doi:10.1112/topo.12021. S2CID 119336098. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Hartnett, Kevin (2023-08-22). "An Old Conjecture Falls, Making Spheres a Lot More Complicated". Quanta Magazine. Retrieved 2023-08-22. <a href="https://www.quantamagazine.org/an-old-conjecture-falls-making-spheres-a-lot-more-complicated-20230822/" target="_blank">https://www.quantamagazine.org/an-old-conjecture-falls-making-spheres-a-lot-more-complicated-20230822/</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Burklund, Robert; Hahn, Jeremy; Levy, Ishan; Schlank, Tomer (2023). "K-theoretic counterexamples to Ravenel's telescope conjecture". arXiv:2310.17459 [math.AT]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> </ol>