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This is a read note of ‘The Chow t-structure on the $\infty$-category of motivic spectra’.I summarized the main content of this paper and organized its logical flow to facilitate the audience’s understanding of the technical details discussed in the subsequent reports.
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This is a read note of ‘The special fiber of the motivic deformation of the stable homotopy category is algebraic’. In this note, I give a summary of the theoretical part of this paper: according to the equivalence between some parts of the $E_2$-pages of two spectral sequences the authors found by computation, an equivalence between two $\infty$-categories which induces the equivalence between two spectral sequences is found. This result shows us a new way of computing the differentials in the Adams spectral sequences.
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Besides reviewing historical development and prerequisites, we present the main ingredients needed for calculations with spectral sequences for this purpose. These include the Bousfield-Kuhn functor, the Goodwillie tower and so on. We then outline current approaches to running such spectral sequences from cohomology to homotopy, as well as indicate specific questions to investigate.