Geodesic
Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e90

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The goal of this note is to prove that Hodge-de Rham degeneration holds for smooth and proper $\mathbf {F}_p$-schemes X with $\dim (\text{X}) assuming that two conditions hold: its category of quasicoherent sheaves admits a lift to the truncated Brown-Peterson spectrum $\mathrm {BP}\langle {n-1}\rangle $, and the Hochschild-Kostant-Rosenberg spectral sequence for X degenerates at the $\mathrm{E}_2$-page. This result is obtained from a noncommutative version thereof, whose proof is essentially the same as Mathew’s argument in [Mat20]. 
Devalapurkar, Sanath K. Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e90. doi: 10.1017/fms.2025.25
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