PreprintarXiv licencearXiv
Borel's computation of the ranks of K-theory revisited
Abstract
We reprove Borel's computation of the rank of the K-groups of rings of algebraic integers 𝒪F for certain number fields, e.g., F = ℚ(μlk) for l an odd regular prime number. The idea is to recover a simple formula for l-adic {é}tale cohomology groups of 𝒪F in terms of Iwasawa theoretic objects without using Borel's result as an input.
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BibTeX
@misc{hesse2026borels,
title = {{Borel's computation of the ranks of $K$-theory revisited}},
author = {Jan Ole Hesse},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26885},
eprint = {2610.26885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26885},
}
RIS
TY - UNPB
TI - Borel's computation of the ranks of K-theory revisited
AU - Jan Ole Hesse
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.26885
UR - https://arxiv.org/abs/2610.26885
AB - We reprove Borel's computation of the rank of the K-groups of rings of algebraic integers 𝒪_F for certain number fields, e.g., F = ℚ(μ_l^k) for l an odd regular prime number. The idea is to recover a simple formula for l-adic {é}tale cohomology groups of 𝒪_F in terms of Iwasawa theoretic objects without using Borel's result as an input.
ER -