A canonical generator for congruence ideals of Hida families
Abstract
Abstract We construct adjoint p -adic L -functions generating the congruence ideal attached to Hida families. These functions interpolate the Petersson norm of any classical ordinary newform, normalized by a product of Shimura’s canonical periods. We show that, after adjusting by suitable Euler factors, they are interpolated by a regular element of Hida’s universal ordinary Hecke algebra. We also establish a link between these p -adic L -functions and the characteristic series of primitive adjoint Selmer groups.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Research in the Mathematical Sciences
- Publisher
- Springer Science and Business Media LLC
- Volume
- 13
- Issue
- 1
- Publication date
- 29 January 2026
- Language
- EN