Anticyclotomic main conjecture and the non-triviality of Rankin–Selberg L-values in Hida families

نویسندگان

چکیده

We prove the two-variable anticyclotomic Iwasawa main conjecture for Hida families and discuss its arithmetic application to a definite version of horizontal non-vanishing conjecture, which is formulated in [LV11]. Our approach based on control theorem Selmer groups relation between L-function built out p-adic Gross points Shimura curves studied [CL16] [CKL17] self-dual twist specialisation line three-variable Skinner–Urban [SU14].

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ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2023

ISSN: ['0022-314X', '1096-1658']

DOI: https://doi.org/10.1016/j.jnt.2023.03.007