YNTOMIC COHOMOLOGY OF DERIVED SCHEMES AND THE MOTIVIC FILTRATION ON TOPOLOGICAL CYCLIC HOMOLOGY
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901107806044160 |
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| author | Revista, Zen MFC, 10 |
| author_facet | Revista, Zen MFC, 10 |
| contents | <div>Mathematical Applications of Science Fiction</div> <div> </div> <p>We construct a symmetric monoidal ∞-category of derived syntomic motives Msyn(X) over<br>a derived scheme X. We define the syntomic cohomology RΓsyn(X, Zp(n)) as mapping objects in this<br>category and establish a canonical equivalence between these cohomology groups and the graded pieces<br>of the motivic filtration on the topological cyclic homology TC(X; p). We extend the Bhatt-Morrow-<br>Scholze filtration to the context of derived algebraic geometry using the formalism of quasisyntomic<br>descent. Finally, we prove that for a quasi-compact quasi-separated derived scheme X, the category of<br>syntomic coefficients admits a Tannakian structure, identifying the motivic Galois group in the p-adic<br>setting.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18100828 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | YNTOMIC COHOMOLOGY OF DERIVED SCHEMES AND THE MOTIVIC FILTRATION ON TOPOLOGICAL CYCLIC HOMOLOGY Revista, Zen MFC, 10 <div>Mathematical Applications of Science Fiction</div> <div> </div> <p>We construct a symmetric monoidal ∞-category of derived syntomic motives Msyn(X) over<br>a derived scheme X. We define the syntomic cohomology RΓsyn(X, Zp(n)) as mapping objects in this<br>category and establish a canonical equivalence between these cohomology groups and the graded pieces<br>of the motivic filtration on the topological cyclic homology TC(X; p). We extend the Bhatt-Morrow-<br>Scholze filtration to the context of derived algebraic geometry using the formalism of quasisyntomic<br>descent. Finally, we prove that for a quasi-compact quasi-separated derived scheme X, the category of<br>syntomic coefficients admits a Tannakian structure, identifying the motivic Galois group in the p-adic<br>setting.</p> |
| title | YNTOMIC COHOMOLOGY OF DERIVED SCHEMES AND THE MOTIVIC FILTRATION ON TOPOLOGICAL CYCLIC HOMOLOGY |
| url | https://doi.org/10.5281/zenodo.18100828 |