Geodesic
ENDOMORPHISMS OF EXOTIC MODELS
Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 321-348

Voir la notice de l'article provenant de la source Cambridge University Press

We calculate the endomorphism dga of Franke's exotic algebraic model for the K-local stable homotopy category at odd primes. We unravel its original abstract structure to give explicit generators, differentials and products. 
ELLIS, EUGENIA; ROITZHEIM, CONSTANZE; SCULL, LAURA; YARNALL, CAROLYN. ENDOMORPHISMS OF EXOTIC MODELS. Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 321-348. doi: 10.1017/S001708951800023X
@article{10_1017_S001708951800023X,
     author = {ELLIS, EUGENIA and ROITZHEIM, CONSTANZE and SCULL, LAURA and YARNALL, CAROLYN},
     title = {ENDOMORPHISMS {OF} {EXOTIC} {MODELS}},
     journal = {Glasgow mathematical journal},
     pages = {321--348},
     year = {2019},
     volume = {61},
     number = {2},
     doi = {10.1017/S001708951800023X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951800023X/}
}
TY  - JOUR
AU  - ELLIS, EUGENIA
AU  - ROITZHEIM, CONSTANZE
AU  - SCULL, LAURA
AU  - YARNALL, CAROLYN
TI  - ENDOMORPHISMS OF EXOTIC MODELS
JO  - Glasgow mathematical journal
PY  - 2019
SP  - 321
EP  - 348
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951800023X/
DO  - 10.1017/S001708951800023X
ID  - 10_1017_S001708951800023X
ER  - 
%0 Journal Article
%A ELLIS, EUGENIA
%A ROITZHEIM, CONSTANZE
%A SCULL, LAURA
%A YARNALL, CAROLYN
%T ENDOMORPHISMS OF EXOTIC MODELS
%J Glasgow mathematical journal
%D 2019
%P 321-348
%V 61
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951800023X/
%R 10.1017/S001708951800023X
%F 10_1017_S001708951800023X

[1] 1. Adams, J. F. and Clarke, F. W., Stable operations on complex K-theory, Ill. J. Math. 21 (1977), 826–829. Google Scholar

[2] 2. Adams, J. F., Harris, A. S. and Switzer, R. M., Hopf algebras of cooperations for real and complex K-theory, Proc. Lond. Math. Soc., s3-23 (1971), 385–408. Google Scholar

[3] 3. Barnes, D. and Roitzheim, C., Local framings, N. Y. J. Math. 17 (2011), 513–552. Google Scholar

[4] 4. Bousfield, A. K., The localization of spectra with respect to homology, Topology 18 (1979), 257–281. Google Scholar

[5] 5. Bousfield, A. K., On the homotopy theory of K-local spectra at an odd prime, Am. J. Math. 107 (1985), 895–932. Google Scholar

[6] 6. Clarke, F., Crossley, M. and Whitehouse, S., Algebras of operations in K-theory, Topology 44 (2005), 151–174. Google Scholar

[7] 7. Dugger, D., Spectral enrichments of model categories, Homol., Homotopy Appl. 8 (2006), 1–30. Google Scholar

[8] 8. Dugger, D., Replacing model categories with simplicial ones. Trans. Am. Math. Soc. 12 (2001), 5003–5027. Google Scholar

[9] 9. Dugger, D. and Shipley, B., Topological equivalences for differential graded algebras, Adv. Math. 212 (2007), 37–61. Google Scholar

[10] 10. Franke, J., Uniqueness theorems for certain triangulated categories possessing an Adams spectral sequence (1996). Available at http://www.math.uiuc.edu/K-theory/0139/. Google Scholar

[11] 11. Hovey, M., Homotopy theory of comodules over a Hopf algebroid, Contemp. Math. 346 (2004), 261–304. Google Scholar

[12] 12. Johnson, K., The algebra of stable operations for complex p-local K-theory, Can. Math. Bull. 30 (1987), 57–62. Google Scholar

[13] 13. Patchkoria, I., On the algebraic classification of module spectra, Algebraic Geom. Topol. 12 (2012), 2329–2388. Google Scholar

[14] 14. Patchkoria, I., On exotic equivalences and a theorem of Franke. Available at https://arxiv.org/pdf/1612.03732.pdf. Google Scholar

[15] 15. Ravenel, D. C.. Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics, vol. 121 (Academic Press Inc., Orlando, FL, 1986). Google Scholar

[16] 16. Roitzheim, C., Rigidity and exotic models for the K-local stable homotopy category. Geom. Topol. 11 (2007), 1855–1886. Google Scholar

[17] 17. Roitzheim, C., On the algebraic classification of K-local spectra, Homology, Homotopy Appl., 10 (2008), 389–412. Google Scholar

[18] 18. Roitzheim, C., A case of monoidal uniqueness of algebraic models, Forum Math. 27 (6) (2015), 3615–3634. Google Scholar

[19] 19. Schwede, S., The stable homotopy category is rigid, Ann. Math. (2), 166 (2007), 837–863. Google Scholar

[20] 20. Schwede, S. and Shipley, B., Stable model categories are categories of modules. Topology 42 (2003), 103–153. Google Scholar

[21] 21. Strong, M. J. and Whitehouse, S., Infinite sums of unstable Adams operations and cobordism, J. Pure Appl. Algebra 214 (2010), 910–918. Google Scholar

Cité par Sources :