Fine Selmer Groups and Isogeny Invariance

Sujatha, R.; Witte, Malte

doi:10.1007/978-3-319-97379-1_19

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…It follows from results of Sujatha and Witte (see [24,Section 3]) that the second definition becomes independent of the choice of Σ as soon as L contains the cyclotomic Z p -extension K c ∞ of K; in fact, in this situation we have Sel 0,A,Σ (L) = Sel 0,A (L)…”

Section: For Any (Not Necessarily Finite) Extensionmentioning

confidence: 99%

Fine Selmer groups of modular forms

Kleine¹,

Müller²

2022

Preprint

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We compare the Iwasawa invariants of fine Selmer groups of p-adic Galois representations over admissible p-adic Lie extensions of a number field K to the Iwasawa invariants of ideal class groups along these Lie extensions.More precisely, let K be a number field, let V be a p-adic representation of the absolute Galois group G K of K, and choose a G K -invariant lattice T ⊆ V . We study the fine Selmer groups of A = V /T over suitable p-adic Lie extensions K∞/K, comparing their corank and µ-invariant to the corank and the µ-invariant of the Iwasawa module of ideal class groups in K∞/K.In the second part of the article, we compare the Iwasawa µ-and l 0invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple Zp-extensions of K.

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Section: For Any (Not Necessarily Finite) Extensionmentioning

confidence: 99%

Fine Selmer groups of modular forms

Kleine¹,

Müller²

2022

Preprint

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“…A priori this definition depends on the choice of Σ. But if the cyclotomic Zextension of , denoted by ∞ , is contained in , then the definition becomes independent of the set Σ by a result of Sujatha and Witte (see [SW18,Section 3]). They also show that in this case the two definitions of the Selmer group given above coincide.…”

Section: Fine Selmer Groupsmentioning

confidence: 99%

Fine Selmer groups of congruent p-adic Galois representations

Kleine

Müller²

2021

Can. Math. Bull.

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We compare the Pontryagin duals of fine Selmer groups of two congruent -adic Galois representations over admissible pro-, -adic Lie extensions ∞ of number fields . We prove that in several natural settings the -primary submodules of the Pontryagin duals are pseudo-isomorphic over the Iwasawa algebra; if the coranks of the fine Selmer groups are not equal, then we can still prove inequalities between the -invariants. In the special case of a Z -extension ∞ / , we also compare the Iwasawa -invariants of the fine Selmer groups, even in situations where the -invariants are non-zero. Finally, we prove similar results for certain abelian non--extensions.

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“…Remark 2.17. In [63], the authors investigate the behavior of Conjecture A under the change of base field, short exact sequences of representations, and isogenies. Moreover, they give various equivalent formulations of Conjecture A and they discuss the relation between Conjecture A and the Iwasawa µ-invariant conjecture in more details.…”

Section: Introduction To Conjecture Amentioning

confidence: 99%

Conjecture A andμ-invariant for Selmer groups of supersingular elliptic curves

Hamidi¹,

Ray²

2022

Journal De Théorie Des Nombres De Bordeaux

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Fine Selmer Groups and Isogeny Invariance

Cited by 3 publications

References 15 publications

Fine Selmer groups of modular forms

Fine Selmer groups of modular forms

Fine Selmer groups of congruent p-adic Galois representations

Conjecture A andμ-invariant for Selmer groups of supersingular elliptic curves

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