PreprintarXiv licencearXiv
Algebraic Eisenstein classes for GLn with applications to the Bianchi case
Abstract
Let L be a number field containing a CM field K. We compute an explicit current representing the GL𝒪K(𝒪L)-equivariant algebraic Eisenstein-Kronecker classes constructed by Kings-Sprang. In the Bianchi case, where K is imaginary quadratic and [L:K]=2, this yields a purely algebraic construction of Eisenstein cohomology classes, even though the associated locally symmetric space is not an algebraic variety. We express their constant terms at the cusp in terms of partial Hecke L-values of K.
Related
- On the Cohomology Classes of Certain Eisenstein-Kronecker Forms
- How many points does an affine algebraic set have in residue classes modulo n ?
- On Universal Minkowski Classes of Polytopes: Theory and Applications
- Characteristic Classes of Adelic Vector Bundles and Applications
- Chern-Schwartz-MacPherson classes of symmetric powers and applications
BibTeX
@misc{du2026algebraic,
title = {{Algebraic Eisenstein classes for $\mathrmGL_n$ with applications to the Bianchi case}},
author = {Zhenghang Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08375},
eprint = {2610.08375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08375},
}
RIS
TY - UNPB
TI - Algebraic Eisenstein classes for GL_n with applications to the Bianchi case
AU - Zhenghang Du
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08375
UR - https://arxiv.org/abs/2610.08375
AB - Let L be a number field containing a CM field K. We compute an explicit current representing the GL_𝒪_K(𝒪_L)-equivariant algebraic Eisenstein-Kronecker classes constructed by Kings-Sprang. In the Bianchi case, where K is imaginary quadratic and [L:K]=2, this yields a purely algebraic construction of Eisenstein cohomology classes, even though the associated locally symmetric space is not an algebraic variety. We express their constant terms at the cusp in terms of partial Hecke L-values of K.
ER -