2014/05/20 by Meng Fai Lim, Lim, Meng Fai
Mathematics · #11F80 #11R23 #11R34 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1405.5289
openalex publication_date 2014/05/20 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28
The main conjecture of Iwasawa theory is a conjecture on the relation between\na Selmer group and a conjectural p-adic L-function. This conjectural\np-adic L-function is expected to satisfy a conjectural functional equation\nin a certain sense. In view of the main conjecture and this conjectural\nfunctional equation, one would expect to have certain algebraic relationship\nbetween the Selmer group attached to a Galois representation and the Selmer\ngroup attached to the Tate twist of the dual of the Galois representation. It\nis precisely a component of this algebraic relationship that this paper aims to\ninvestigate. Namely, for a given "ordinary" p-adic representation, we compare\nits Selmer group with the Selmer group of its Tate dual over an admissible\np-adic Lie extension, and show that the generalized Iwasawa \μ-invariants\nassociated to the Pontryagin dual of the two said Selmer groups are the same.\nWe should mention that in proving the said equality of the \μ-invariants, we\ndo not assume the main conjecture nor the conjectural functional equation.\n