This article formulates a -adic analogue of the Birch and Swinnerton-Dyer conjecture for a -adic -function associated to a triple of Hida families of modular forms. This involves the construction of a -adic regulator, obtained by building on Nekovář theory of Selmer complexes. Moreover, it is proved that our conjectures imply the “Elliptic Stark Conjectures” of Darmon, Lauder and Rotger.
On p-adic analogues of the Birch and Swinnerton-Dyer conjecture for Garrett L-functions / M. Bertolini, M.A. Seveso, R. Venerucci. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 0373-0956. - (2025), pp. 1-35. [Epub ahead of print] [10.5802/aif.3726]
On p-adic analogues of the Birch and Swinnerton-Dyer conjecture for Garrett L-functions
M. BertoliniPrimo
;M.A. SevesoSecondo
;R. VenerucciUltimo
2025
Abstract
This article formulates a -adic analogue of the Birch and Swinnerton-Dyer conjecture for a -adic -function associated to a triple of Hida families of modular forms. This involves the construction of a -adic regulator, obtained by building on Nekovář theory of Selmer complexes. Moreover, it is proved that our conjectures imply the “Elliptic Stark Conjectures” of Darmon, Lauder and Rotger.
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