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- Title
Eisenstein cohomology classes for GL<sub>N</sub> over imaginary quadratic fields.
- Authors
Bergeron, Nicolas; Charollois, Pierre; García, Luis E.
- 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.
- Subjects
QUADRATIC fields; DEDEKIND sums; SYMMETRIC spaces; EISENSTEIN series; ELLIPTIC curves; ARITHMETIC; L-functions
- Publication
Journal für die Reine und Angewandte Mathematik, 2023, Vol 2023, Issue 797, p1
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2022-0089