Iwasawa theory of the fine Selmer group

DOI10.1090/S1056-3911-06-00436-XzbMath1110.11034MaRDI QIDQ3424128

Christian Wuthrich

Publication date: 15 February 2007

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

zbMATH Keywords

Iwasawa theoryTate-Shafarevich groupSelmer group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Iwasawa theory (11R23)

Related Items (22)

On the weak Leopoldt conjecture and coranks of Selmer groups of supersingular abelian varieties in \(p\)-adic Lie extensions ⋮ On order of vanishing of characteristic elements ⋮ ON FINE SELMER GROUPS AND SIGNED SELMER GROUPS OF ELLIPTIC MODULAR FORMS ⋮ Unnamed Item ⋮ On the \(\mu\)-invariant of fine Selmer groups ⋮ Arithmetic statistics for the fine Selmer group in Iwasawa theory ⋮ Control theorems for fine Selmer groups ⋮ On the corank of the fine Selmer group of an elliptic curve over a \(\mathbb{Z}_p\)-extension ⋮ Structure of fine Selmer groups in abelian \(p\)-adic Lie extensions ⋮ Structure of fine Selmer groups over -extensions ⋮ On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in \(\mathbb{Z}_p\)-extensions ⋮ On the Hida deformations of fine Selmer groups ⋮ Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions ⋮ Fine Selmer groups of congruent Galois representations ⋮ Anticyclotomic \(\mu \)-invariants of residually reducible Galois representations ⋮ Conjecture a and \(\mu\)-invariant for Selmer groups of supersingular elliptic curves ⋮ Algorithms for the arithmetic of elliptic curves using Iwasawa theory ⋮ On fine Selmer groups and the greatest common divisor of signed and chromatic 𝑝-adic 𝐿-functions ⋮ Bounding the Iwasawa invariants of Selmer groups ⋮ Fine Selmer Groups and Isogeny Invariance ⋮ Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms ⋮ On universal norms for $p$-adic representations in higher-rank Iwasawa theory

Cites Work

• Unnamed Item
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• \(p\)-adic height pairings. II
• Iwasawa theory and \(p\)-adic heights
• \(p\)-adic \(L\)-functions of an elliptic curve and rational points
• Iwasawa theory for elliptic curves at supersingular primes
• On the \(p\)-adic \(L\)-function of a modular form at a supersingular prime
• Fine Selmer groups of elliptic curves over \(p\)-adic Lie extensions
• Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields
• A remark on the rational points of abelian varieties with values in cyclotomic $Z_p$-extensions
• ON ${p}$-ADIC HEIGHTS IN FAMILIES OF ELLIPTIC CURVES
• Euler Systems
• Galois cohomology of elliptic curves

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