Motivic Cohomology and K-groups of varieties over higher local fields
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915880737177600 |
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| author | Gupta, Rahul Krishna, Amalendu Rathore, Jitendra |
| author_facet | Gupta, Rahul Krishna, Amalendu Rathore, Jitendra |
| contents | For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups for smooth projective varieties over such fields, where $p$ denotes the final residue characteristic of $k_N$. As an application, we show that the kernel of the tame reciprocity map is uniquely $p'$-divisible. A key ingredient in achieving these results is the finiteness of étale cohomology groups over such fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_21000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Motivic Cohomology and K-groups of varieties over higher local fields Gupta, Rahul Krishna, Amalendu Rathore, Jitendra Algebraic Geometry Primary 14C25, Secondary 14F30 For quasi-projective varieties over a higher local field $k_N$, we prove that its $K$-groups, above a suitable degree, are divisible-by-finite. We also prove the finiteness of the prime-to-$p$ torsion subgroup of certain higher Chow groups for smooth projective varieties over such fields, where $p$ denotes the final residue characteristic of $k_N$. As an application, we show that the kernel of the tame reciprocity map is uniquely $p'$-divisible. A key ingredient in achieving these results is the finiteness of étale cohomology groups over such fields. |
| title | Motivic Cohomology and K-groups of varieties over higher local fields |
| topic | Algebraic Geometry Primary 14C25, Secondary 14F30 |
| url | https://arxiv.org/abs/2603.21000 |