Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case

Zhenghang Du

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arXiv · 2610.08375

Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case

Zhenghang Du

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Abstract

Let $L$ be a number field containing a CM field $K$. We compute an explicit current representing the $\mathrm{GL}_{\mathcal{O}_K}(\mathcal{O}_L)$-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 $K$.

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BibTeX RIS

Zhenghang Du. 2026-10-06. Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case. https://arxiv.org/abs/2610.08375

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