PreprintCC BY-NC-ND 4.0arXiv
The Morita classes are nonzero
Abstract
We prove that all Morita classes μk ∈ H4k(Aut(F2k+2);ℚ) are nonzero using a novel description of the Hopf algebra structure on Steinberg homology. We prove analogous results with twisted coefficients. Our results disprove a case of a finiteness conjecture of Kontsevich.
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BibTeX
@misc{kupers2026morita,
title = {{The Morita classes are nonzero}},
author = {Alexander Kupers and Jeremy Miller and Peter Patzt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12951},
eprint = {2609.12951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12951},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Morita classes are nonzero
AU - Alexander Kupers
AU - Jeremy Miller
AU - Peter Patzt
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12951
UR - https://arxiv.org/abs/2609.12951
AB - We prove that all Morita classes μ_k ∈ H_4k(Aut(F_2k+2);ℚ) are nonzero using a novel description of the Hopf algebra structure on Steinberg homology. We prove analogous results with twisted coefficients. Our results disprove a case of a finiteness conjecture of Kontsevich.
ER -