Abstract
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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Acknowledgments
We are grateful to A. Efimov, A. Fonarev, L. Hesselholt, Th. Nikolaus, and A. Prihodko for useful discussions. We thank MSRI, where part of this work was done. We are also especially grateful to A. Mathew for generously sharing his insights and expertise, and in particular for helping us with (the sketch of) the proof of Proposition 2.3.
Funding
The work was supported in part by the BASIS Foundation, project no. 18-1-6-95-1, Leader (Math). The first two authors were also supported by the HSE Basic Research Program and the Russian Academic Excellence Project “5-100.”
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To the blessed memory of I. R. Shafarevich
This article was submitted by the authors simultaneously in Russian and English
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 307, pp. 63–77.
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Kaledin, D.B., Konovalov, A.A. & Magidson, K.O. Spectral Algebras and Non-commutative Hodge-to-de Rham Degeneration. Proc. Steklov Inst. Math. 307, 51–64 (2019). https://doi.org/10.1134/S0081543819060038
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DOI: https://doi.org/10.1134/S0081543819060038