Bergeron, Nicolas;
Charollois, Pierre;
García, Luis E;
(2023)
Eisenstein cohomology classes for GL_{N} over imaginary quadratic fields.
Journal für die reine und angewandte Mathematik (Crelles Journal)
, 797
pp. 1-40.
10.1515/crelle-2022-0089.
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Abstract
We study the arithmetic of degree N − 1 Eisenstein cohomology classes for the locally symmetric spaces attached to GL_{N} over an imaginary quadratic field k. Under natural conditions we evaluate these classes on (N − 1) -cycles associated to degree N extensions L/k as linear combinations of generalized Dedekind sums. As a consequence we prove a remarkable conjecture of Sczech and Colmez expressing critical values of L-functions attached to Hecke characters of L as polynomials in Kronecker–Eisenstein series evaluated at torsion points on elliptic curves with complex multiplication by k. We recover in particular the algebraicity of these critical values.
| Type: | Article |
|---|---|
| Title: | Eisenstein cohomology classes for GL_{N} over imaginary quadratic fields |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/crelle-2022-0089 |
| Publisher version: | https://doi.org/10.1515/crelle-2022-0089 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10183131 |
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