Eisenstein cocycles for GL(n) and values of L-functions in imaginary quadratic extensions

We generalize Sczech's Eisenstein cocycle for \(\mathrm{GL}(n)\) over totally real extensions of \(\mathbb{Q}\) to finite extensions of imaginary quadratic fields. By evaluating the cocycle on certain cycles, we parametrize complex values of Hecke L-functions previously considered by Colmez, gi...

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Bibliographic Details
Published in:arXiv.org 2020-01
Main Authors: Flórez, Jorge, Karabulut, Cihan, Tian An Wong
Format: Article
Language:English
Subjects:
Algebra
Fields (mathematics)
Number theory
Online Access:Get full text
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Summary:We generalize Sczech's Eisenstein cocycle for \(\mathrm{GL}(n)\) over totally real extensions of \(\mathbb{Q}\) to finite extensions of imaginary quadratic fields. By evaluating the cocycle on certain cycles, we parametrize complex values of Hecke L-functions previously considered by Colmez, giving a cohomological interpretation of his algebraicity result on special values of the L-functions.
ISSN:2331-8422
DOI:10.48550/arxiv.1611.08565