\(p\)-Selmer group and modular symbols

DOI10.25537/dm.2022v27.1891-1922MaRDI QIDQ2095956

Ryotaro Sakamoto

Publication date: 15 November 2022

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.03370

zbMATH Keywords

elliptic curvesmodular symbolsEuler systemsKolyvagin systems\(p\)-Selmer groupMazur-Tate conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Galois cohomology (11R34)

Cites Work

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• Controlling Selmer groups in the higher core rank case
• Stickelberger elements and modular parametrizations of elliptic curves
• Refined conjectures of the ``Birch and Swinnerton-Dyer type
• Iwasawa theory of \(p\)-adic representations over a local field
• On the structure of ideal class groups of CM-fields
• Stark systems over Gorenstein local rings
• Equivariant Iwasawa theory for elliptic curves
• On the theory of Kolyvagin systems of rank 0
• On the indivisibility of derived Kato's Euler systems and the main conjecture for modular forms
• Remarks on Kato's Euler systems for elliptic curves with additive reduction
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• On the parity of ranks of Selmer groups II
• A generalized Mazur’s theorem and its applications
• Kolyvagin systems
• Kato's Euler system and the Mazur-Tate refined conjecture of BSD type
• Euler Systems
• On the Theory of Higher Rank Euler, Kolyvagin and Stark Systems
• The Structure of Selmer Groups of Elliptic Curves and Modular Symbols

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