A Study of Fine Selmer Groups Over Function Fields via Greenberg Neighbourhoods

2025/06/27 by Ghosh, Sohan
#11G05 #11R58 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11R23 #Secondary: 20C07

paper · doi:10.48550/arxiv.2506.22002

Abstract

Greenberg examined the local behavior of Iwasawa invariants as functions on the the set of all ℤ_p-extensions of a number field F. Kleine later extended these ideas to explore the variation of Iwasawa invariants in the context of Selmer groups of elliptic curves across different ℤ_p-extensions of F. Let K be a global function field of characteristic p. In this article, we investigate the relation between Iwasawa invariants of fine Selmer groups of an elliptic curve over K across various ℤ_p-extensions of K, utilizing Kleine's techniques. Furthermore, we connect this analysis to an analogue of Conjecture A by Coates and Sujatha for different ℤ_p-extensions of the function field K.

Citations

• Iwasawa theory of fine Selmer groups over global fields
• Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p

Related

• Iwasawa theory of fine Selmer groups over global fields
• On the Pseudonullity of Fine Selmer groups over function fields
• Aspects of Iwasawa theory over function fields
• The Iwasawa μ-invariants of Elliptic Curves over ℚ
• Iwasawa theory for elliptic curves at supersingular primes over Z_p-extensions of number fields