Fine Selmer group of Hida deformations over non-commutative $p$-adic Lie extensions
| Autor: | Somnath Jha |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
non-commutative Iwasawa theory 11F80 Selmer group Galois cohomology General Mathematics Fundamental theorem of Galois theory Mathematics::Number Theory Galois group Context (language use) symbols.namesake 14G05 Mathematics Discrete mathematics Group (mathematics) Applied Mathematics $p$-adic Galois representation Hida theory 16E40 11F33 Galois module Elliptic curve 11R23 symbols 11G05 congruences of modular forms |
| Zdroj: | Asian J. Math. 16, no. 2 (2012), 353-366 |
| Popis: | We study the Selmer group and the fine Selmer group of $p$-adic Galois representations defined over a non-commutative $p$-adic Lie extension and their Hida deformations. For the fine Selmer group, we generalize the pseudonullity conjecture of J. Coates and R. Sujatha, "Fine Selmer group of elliptic curves over $p$-adic Lie extensions," in this context and discuss its invariance in a branch of a Hida family. We relate the structure of the ‘big’ Selmer (resp. fine Selmer) group with the specialized individual Selmer (resp. fine Selmer) groups. |
| Databáze: | OpenAIRE |
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