Non-critical p-adic twisted adjoint L-function for ordinary families on definite unitary groups
Abstract
Let F/Q be an imaginary quadratic extension, let χ_{F/Q} be the associated quadratic character, let p be split in F, and let G be a definite unitary group of odd rank n. We construct a p-adic twisted adjoint L-function attached to an ordinary Hida family on G, interpolating the non-critical values L^imp(Π_P, Ad ⊗ χ_{F/Q}, 1) at its regular arithmetic specializations P. The construction proceeds through conjugate self-dual stable base change to GL_n(A_F) and realizes the twisted adjoint value as a residue of an Asai L-function via the Flicker–Rallis period. At p, we obtain the Coates–Perrin-Riou modifying factor by translating the ordinary test vector. We interpolate the resulting periods using distribution-valued ordinary cohomology. Under suitable Calegari–Geraghty hypotheses, the specialization defect is identified with the Fitting ideal of a congruence module. Finally, we construct stable base change on localized universal ordinary Hecke algebras and obtain the desired p-adic L-function on the Hida family on the unitary group.
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BibTeX
@misc{wang2026noncritical,
title = {{Non-critical p-adic twisted adjoint L-function for ordinary families on definite unitary groups}},
author = {Zheng Wang},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05775268v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-critical p-adic twisted adjoint L-function for ordinary families on definite unitary groups
AU - Zheng Wang
PY - 2026
DA - 2026/10/24
PB - HAL
UR - https://hal.science/hal-05775268v2
AB - Let F/Q be an imaginary quadratic extension, let χ_{F/Q} be the associated quadratic character, let p be split in F, and let G be a definite unitary group of odd rank n. We construct a p-adic twisted adjoint L-function attached to an ordinary Hida family on G, interpolating the non-critical values L^imp(Π_P, Ad ⊗ χ_{F/Q}, 1) at its regular arithmetic specializations P. The construction proceeds through conjugate self-dual stable base change to GL_n(A_F) and realizes the twisted adjoint value as a residue of an Asai L-function via the Flicker–Rallis period. At p, we obtain the Coates–Perrin-Riou modifying factor by translating the ordinary test vector. We interpolate the resulting periods using distribution-valued ordinary cohomology. Under suitable Calegari–Geraghty hypotheses, the specialization defect is identified with the Fitting ideal of a congruence module. Finally, we construct stable base change on localized universal ordinary Hecke algebras and obtain the desired p-adic L-function on the Hida family on the unitary group.
ER -