Geodesic
Spectral Algebras and Non-commutative Hodge-to-de Rham Degeneration
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 63-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

We revisit the non-commutative Hodge-to-de Rham degeneration theorem of the first author and present its proof in a somewhat streamlined and improved form that explicitly uses spectral algebraic geometry. We also try to explain why topology is essential to the proof. 
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     author = {D. B. Kaledin and A. A. Konovalov and K. O. Magidson},
     title = {Spectral {Algebras} and {Non-commutative} {Hodge-to-de} {Rham} {Degeneration}},
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D. B. Kaledin; A. A. Konovalov; K. O. Magidson. Spectral Algebras and Non-commutative Hodge-to-de Rham Degeneration. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 63-77. http://geodesic.mathdoc.fr/item/TM_2019_307_a2/

[1] Connes A., “Cohomologie cyclique et foncteurs $\mathrm {Ext}^n$”, C. r. Acad. sci. Paris. Sér. 1, 296 (1983), 953–958 | MR | Zbl

[2] Deligne P., Illusie L., “Relèvements modulo $p^2$ et décomposition du complexe de de Rham”, Invent. math., 89 (1987), 247–270 | DOI | MR | Zbl

[3] Drinfeld V., “On the notion of geometric realization”, Moscow Math. J., 4:3 (2004), 619–626 | DOI | MR | Zbl

[4] Kaledin D., “Non-commutative Hodge-to-de Rham degeneration via the method of Deligne–Illusie”, Pure Appl. Math. Q., 4:3 (2008), 785–875 | DOI | MR | Zbl

[5] Kaledin D., “Spectral sequences for cyclic homology”, Algebra, geometry, and physics in the 21st century: Kontsevich Festschrift, Prog. Math., 324, Birkhäuser, Basel, 2017, 99–129 | DOI | MR | Zbl

[6] Kaledin D., “Co-periodic cyclic homology”, Adv. Math., 334 (2018), 81–150 | DOI | MR | Zbl

[7] Kontsevich M., Soibelman Y., Notes on $A_\infty $-algebras, $A_\infty $-categories and non-commutative geometry. I, E-print, 2006, arXiv: math/0606241 [math.RA] | MR

[8] Lurie J., Higher algebra, Preprint, Inst. Adv. Stud., Princeton, NJ, 2017 https://www.math.ias.edu/~lurie/papers/HA.pdf

[9] Mathew A., Kaledin's degeneration theorem and topological Hochschild homology, E-print, 2017, arXiv: 1710.09045 [math.KT] | MR

[10] Nikolaus T., Scholze P., On topological cyclic homology, E-print, 2017, arXiv: 1707.01799 [math.AT] | MR

[11] Segal G., “Configuration-spaces and iterated loop-spaces”, Invent. math., 21 (1973), 213–221 | DOI | MR | Zbl

[12] Toën B., Anneaux de définition des dg-algèbres propres et lisses, E-print, 2006, arXiv: math/0611546 [math.AT] | MR