Kings, Guido and Sprang, Johannes (2025) Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation. ANNALS OF MATHEMATICS, 202 (1). pp. 1-109. ISSN 0003-486X, 1939-8980
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We show that for an arbitrary totally complex number field L the (regularized) critical L-values of algebraic Hecke characters of L divided by certain periods are algebraic integers. This relies on a new construction of an equivariant coherent cohomology class with values in the completion of the Poincare<acute accent> bundle on an abelian scheme A. From this we obtain a cohomology class for the automorphism group of a CM abelian scheme A with values in some canonical bundles, which can be explicitly calculated in terms of Eisenstein-Kronecker series. As a further consequence, using an infinitesimal trivialization of the Poincare<acute accent> bundle, we construct a p-adic measure interpolating the critical L-values in the ordinary case. This generalizes previous results for CM fields by Damerell, Shimura and Katz and settles the algebraicity and p-adic interpolation in the remaining open cases of critical values of Hecke L-functions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | COCYCLES; L-values of Hecke characters; Eisenstein co cycles; p-adic L-functions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Apr 2026 06:32 |
| Last Modified: | 15 Apr 2026 06:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65855 |
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