PreprintCC BY-NC-ND 4.0arXiv
On Frobenius rigidity for motivic cohomology
Abstract
We study how motivic and étale motivic cohomology of a smooth and proper variety changes under extensions of algebraically closed base fields k. With finite coefficients, motivic cohomology is independent of k, and étale motivic cohomology is independent of k away from the characteristic, but depends on k at the characteristic. We then consider the fiber of F−1 for F the Frobenius, on motivic cohomology and étale motivic cohomology for varieties defined over finite fields. We show that this fiber is independent of k with finite coefficients. In addition, we give some results and examples with integral coefficients.
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BibTeX
@misc{geisser2026frobenius,
title = {{On Frobenius rigidity for motivic cohomology}},
author = {Thomas H. Geisser},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.27834},
eprint = {2608.27834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27834},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On Frobenius rigidity for motivic cohomology
AU - Thomas H. Geisser
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.27834
UR - https://arxiv.org/abs/2608.27834
AB - We study how motivic and étale motivic cohomology of a smooth and proper variety changes under extensions of algebraically closed base fields k. With finite coefficients, motivic cohomology is independent of k, and étale motivic cohomology is independent of k away from the characteristic, but depends on k at the characteristic. We then consider the fiber of F−1 for F the Frobenius, on motivic cohomology and étale motivic cohomology for varieties defined over finite fields. We show that this fiber is independent of k with finite coefficients. In addition, we give some results and examples with integral coefficients.
ER -