PreprintCC BY 4.0arXiv
On the Motivic K-Theories of Classifying Spaces of Cyclic 2-Groups
Abstract
We compute the $2$-completed integral motivic homology, effective algebraic K-theory, and very effective Hermitian K-theory of the geometric classifying spaces Bμ2n, n≥ 2, over algebraically closed and real closed fields. We first carry out the corresponding classical calculations and, then obtain the motivic results using motivic spectral sequences and comparison techniques. The results reveal the classical $2$-torsion together with motivic τ-periodicity and ρ-torsion.
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BibTeX
@misc{dhankhar2026motivic,
title = {{On the Motivic K-Theories of Classifying Spaces of Cyclic 2-Groups}},
author = {Prerna Dhankhar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27016},
eprint = {2610.27016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27016},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Motivic K-Theories of Classifying Spaces of Cyclic 2-Groups
AU - Prerna Dhankhar
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27016
UR - https://arxiv.org/abs/2610.27016
AB - We compute the $2$-completed integral motivic homology, effective algebraic K-theory, and very effective Hermitian K-theory of the geometric classifying spaces Bμ_2^n, n≥ 2, over algebraically closed and real closed fields. We first carry out the corresponding classical calculations and, then obtain the motivic results using motivic spectral sequences and comparison techniques. The results reveal the classical $2$-torsion together with motivic τ-periodicity and ρ-torsion.
ER -