p -adic interpolation of Gauss–Manin connections on nearly overconvergent modular forms and p -adic L -functions

Journal article

In this paper, we give a new geometric definition of nearly overconvergent modular forms and p-adically interpolate the Gauss–Manin connection on this space. This can be seen as an ‘overconvergent’ version of the unipotent circle action on the space of p-adic modular forms, as constructed by Gouvêa and Howe. This improves on results of Andreatta and Iovita and has applications to the construction of Rankin–Selberg and triple-product p-adic L-functions.

Authors: Graham, A; Pilloni, V; Rodrigues Jacinto, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Compositio Mathematica
• Volume: 161
• Issue: 9
• Pages: 2380-2441
• Publication date: 2025-11-05
• Acceptance date: 2025-05-12
• DOI: 10.1112/s0010437x25102479
• EISSN: 1570-5846
• ISSN: 0010437X, 0010-437X
• Language: English
• Keywords: Coleman families; modular forms; 11F67; p-adic L-functions; Gauss–Manin connections; modular curves; 11F33; 11F77