On Ribet's lemma for \(\mathrm{GL}_2\) modulo prime powers

DOI10.1007/s40687-023-00419-6arXiv2111.01559WikidataQ124801732 ScholiaQ124801732MaRDI QIDQ6202881

Amit Ophir, Ariel Weiss

Publication date: 27 February 2024

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.01559

zbMATH Keywords

Bruhat-Tits treesrepresentations over discretely valued fieldsRibet's lemma

Mathematics Subject Classification ID

Integral representations (11S23) (p)-adic representations of finite groups (20C11) Elliptic curves over global fields (11G05) Linear algebraic groups over local fields and their integers (20G25) Groups acting on trees (20E08)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Subgroups of \(\mathrm{GL}_2\) and trees.
• Tetrahedral elliptic curves and the local-global principle for isogenies
• Powerful \(p\)-groups. II: \(p\)-adic analytic groups
• A local-global principle for rational isogenies of prime degree
• Representations on a complete discrete valuation ring.
• Galois properties of torsion points on abelian varieties
• A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
• On residually reducible representations on local rings
• Selmer groups and the Eisenstein-Klingen ideal.
• On a lemma of Ribet.
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• The Iwasawa conjecture for totally real fields
• The p-adic analytic space of pseudocharacters of a profinite group and pseudorepresentations over arbitrary rings
• A local‐global principle for isogenies of composite degree
• Residually reducible representations of algebras over local Artinian rings
• A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
• A local-global principle for isogenies of prime degree over number fields

This page was built for publication: On Ribet's lemma for \(\mathrm{GL}_2\) modulo prime powers