Yntomic Cohomology of Derived Schemes and the Motivic Filtration on Topological Cyclic Homology
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We construct a symmetric monoidal ∞-category of derived syntomic motives Msyn(X) overa derived scheme X. We define the syntomic cohomology RΓsyn(X, Zp(n)) as mapping objects in thiscategory and establish a canonical equivalence between these cohomology groups and the graded piecesof the motivic filtration on the topological cyclic homology TC(X; p). We extend the Bhatt-Morrow-Scholze filtration to the context of derived algebraic geometry using the formalism of quasisyntomicdescent. Finally, we prove that for a quasi-compact quasi-separated derived scheme X, the category ofsyntomic coefficients admits a Tannakian structure, identifying the motivic Galois group in the p-adicsetting.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117730009
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