2015/04/12 by Somnath Jha, Jha, Somnath, Dipramit Majumdar +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1504.02959
openalex publication_date 2015/04/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We establish a duality result proving the `functional equation' of the\ncharacteristic ideal of the Selmer group associated to a nearly ordinary\nHilbert modular form over the cyclotomic \ℤp extension of a\ntotally real number field. Further, we use this result to establish a duality\nor algebraic `functional equation' for the `big' Selmer groups associated to\nthe corresponding nearly ordinary Hida deformation. The multivariable\ncyclotomic Iwasawa main conjecture for nearly ordinary Hida family of Hilbert\nmodular forms is not established yet and this can be thought of as an evidence\nto the validity of this Iwasawa main conjecture. We also prove a functional\nequation for the `big' Selmer group associated to an ordinary Hida family of\nelliptic modular forms over the \ℤp2 extension of an imaginary\nquadratic field.\n