PreprintarXiv licencearXiv
On motivic cohomology of commutative C*-algebras
Abstract
Consider the ring of complex-valued continuous functions on a compact Hausdorff space X. Cortiñas--Thom computed its nonpositive algebraic K-theory, confirming Rosenberg's expectation. We give a motivic refinement of their result: For i≥ 2j≥ 0, the ith integral motivic cohomology group of weight j is naturally isomorphic to the ith Betti cohomology group of X.
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BibTeX
@misc{aoki2026motivic,
title = {{On motivic cohomology of commutative C*-algebras}},
author = {Ko Aoki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17621},
eprint = {2609.17621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17621},
}
RIS
TY - UNPB
TI - On motivic cohomology of commutative C*-algebras
AU - Ko Aoki
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.17621
UR - https://arxiv.org/abs/2609.17621
AB - Consider the ring of complex-valued continuous functions on a compact Hausdorff space X. Cortiñas--Thom computed its nonpositive algebraic K-theory, confirming Rosenberg's expectation. We give a motivic refinement of their result: For i≥ 2j≥ 0, the ith integral motivic cohomology group of weight j is naturally isomorphic to the ith Betti cohomology group of X.
ER -