2022/01/05 by Sohan Ghosh, Somnath Jha, Ghosh, Sohan +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry
paper · pdf · doi:10.1007/s00209-025-03863-y
The p^∞-fine Selmer group of an elliptic curve E over a number field F is a subgroup of the classical p^∞-Selmer group of E over F. Fine Selmer group is closely related to the 1st and 2nd Iwasawa cohomology groups. Coates-Sujatha observed that the structure of the fine Selmer group of E over a p-adic Lie extension of a number field is intricately related to some deep questions in classical Iwasawa theory; for example, Iwasawa's classical μ-invariant vanishing conjecture. In this article, we study the properties of the p^∞-fine Selmer group of an elliptic curve over certain p-adic Lie extensions of a number field. We also define and discuss p^∞-fine Selmer group of an elliptic curve over function fields of characteristic p and also of characteristic ℓ ≠ p. We relate our study with a conjecture of Jannsen.