We exemplify in the toy case of generalized Heegner cycles how the methods of [10] yield p-adic interpolation of generalized Heegner classes and deduce a reciprocity law relating the resulting big class to the p-adic L-function constructed in [5]. We also discuss exceptional zero phenomena of these classes and how they can be improved along suitable lines.
Reciprocity Laws for Generalized Heegner Classes / M.A. Seveso (SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS). - In: Elliptic Curves and Modular Forms in Arithmetic Geometry / [a cura di] M. Longo, M.A. Seveso, R. Venerucci, S. Vigni. - [s.l] : Springer Cham, 2026 May 11. - ISBN 9783032131225. - pp. 349-376 (( Celebrating Massimo Bertolini's 60th Birthday Milano 2022 [10.1007/978-3-032-13123-2_12].
Reciprocity Laws for Generalized Heegner Classes
M.A. Seveso
2026
Abstract
We exemplify in the toy case of generalized Heegner cycles how the methods of [10] yield p-adic interpolation of generalized Heegner classes and deduce a reciprocity law relating the resulting big class to the p-adic L-function constructed in [5]. We also discuss exceptional zero phenomena of these classes and how they can be improved along suitable lines.
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