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arXiv · 2603.21000

Motivic Cohomology and K-groups of varieties over higher local fields

Rahul Gupta·Amalendu Krishna·Jitendra Rathore
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Abstract

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 \'etale cohomology groups over such fields.

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Rahul Gupta, Amalendu Krishna, Jitendra Rathore. 2026-03-22. Motivic Cohomology and K-groups of varieties over higher local fields. https://arxiv.org/abs/2603.21000

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