PreprintCC BY 4.0arXiv
Non-vanishing mod p of derived Hecke algebras of multiplicative groups over number fields, II
Abstract
We investigate the derived Hecke action on the cohomology of an arithmetic manifold associated to the multiplicative group over a number field. Under mild assumptions, we prove that the derived Hecke action is non-vanishing modulo p in every degree. Moreover, the total cohomology ring with 𝔽p-coefficients is a free graded module of rank one over the derived Hecke algebra, generated in degree zero.
Related
- Commutator identities, Lie product identities, and Multiplicative Lie algebras
- Hochschild theory of multiplicative sequences of algebras and coalgebra measurings
- Classification of Nijenhuis operators on three-dimensional multiplicative simple Bihom-Lie algebras
- Multiplicative Colombeau algebras and the Nyman--Beurling criterion for the Riemann hypothesis
- Commutative algebras satisfying univariate identities with vanishing Peirce polynomial
BibTeX
@misc{kwon2026nonvanishing,
title = {{Non-vanishing mod $p$ of derived Hecke algebras of multiplicative groups over number fields, II}},
author = {Jaesung Kwon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21278},
eprint = {2610.21278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21278},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-vanishing mod p of derived Hecke algebras of multiplicative groups over number fields, II
AU - Jaesung Kwon
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21278
UR - https://arxiv.org/abs/2610.21278
AB - We investigate the derived Hecke action on the cohomology of an arithmetic manifold associated to the multiplicative group over a number field. Under mild assumptions, we prove that the derived Hecke action is non-vanishing modulo p in every degree. Moreover, the total cohomology ring with 𝔽_p-coefficients is a free graded module of rank one over the derived Hecke algebra, generated in degree zero.
ER -