Controlling Selmer groups in the higher core rank case

DOI10.5802/jtnb.933zbMath1411.11065arXiv1312.4052OpenAlexW2963475208MaRDI QIDQ284485

Barry Mazur, Karl Rubin

Publication date: 18 May 2016

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4052

zbMATH Keywords

Selmer groupsEuler systemscore rankKolyvagin systems

Mathematics Subject Classification ID

Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Galois cohomology (11R34)

Related Items (11)

Iwasawa theory of Rubin-Stark units and class groups ⋮ Refined class number formulas for \(\mathbb{G}_m\) ⋮ Adelic Euler systems for \(\mathbb{G}_m\) ⋮ Strong Selmer companion elliptic curves ⋮ The work of Barry Mazur ⋮ Stark systems over Gorenstein local rings ⋮ Integral Iwasawa theory of Galois representations for non-ordinary primes ⋮ ON IWASAWA THEORY OF RUBIN–STARK UNITS AND NARROW CLASS GROUPS ⋮ On the theory of Kolyvagin systems of rank 0 ⋮ \(p\)-Selmer group and modular symbols ⋮ Théorie d’Iwasawa des unités de Stark et groupe de classes

Cites Work

• Unnamed Item
• Refined class number formulas for \(\mathbb{G}_m\)
• A generalization of Darmon's conjecture for Euler systems for general \(p\)-adic representations
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Iwasawa theory and \(p\)-adic heights
• Systèmes d'Euler \(p\)-adiques et théorie d'Iwasawa. (\(p\)-adic Euler systems and Iwasawa theory.)
• Modular elliptic curves and Fermat's Last Theorem
• A Stark conjecture ``over \({\mathbb{Z}}\) for abelian \(L\)-functions with multiple zeros
• Kolyvagin systems
• Euler Systems

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