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Prismatic and syntomic cohomology of ring spectra

By Jeremy Hahn

Appears in collection : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

I will explain a construction of the motivic filtration on the topological cyclic homology of ring spectra, generalizing work of Bhatt–Morrow–Scholze and Bhatt–Lurie on the topological cyclic homology of discrete rings. This is joint with Arpon Raksit and Dylan Wilson. As time permits, I will discuss works in progress using the motivic spectral sequence to obtain new calculations in algebraic $K$-theory and prove higher chromatic variants of local Tate duality.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19997103
  • Cite this video Hahn, Jeremy (24/01/2023). Prismatic and syntomic cohomology of ring spectra. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19997103
  • URL https://dx.doi.org/10.24350/CIRM.V.19997103

Bibliography

  • HAHN, Jeremy, RAKSIT, Arpon, et WILSON, Dylan. A motivic filtration on the topological cyclic homology of commutative ring spectra. arXiv preprint arXiv:2206.11208, 2022. - https://doi.org/10.48550/arXiv.2206.11208

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