An irreducibility criterion for supersingular $\mathbf{mod}$ $p$ representations of $\operatorname{GL}_{2}(F)$ for totally ramified extensions $F$ of $\mathbb{Q}_{p}$

DOI10.1090/S0002-9947-2011-05478-4zbMath1285.11141OpenAlexW1566667160MaRDI QIDQ3103842

Michael M. Schein

Publication date: 12 December 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05478-4

zbMATH Keywords

Galois representationssupersingular representationsmod \(p\) local Langlands correspondence

Mathematics Subject Classification ID

Galois representations (11F80) Langlands-Weil conjectures, nonabelian class field theory (11S37)

Related Items (7)

On the universal mod \(p\) supersingular quotients for \(\mathrm{GL}_{2}(F)\) over \(\overline{\mathbb{F}}_p\) for a general \(F/\mathbb{Q}_p\) ⋮ On the universal supersingular mod \(p\) representations of \(\mathrm{GL}_2(F)\) ⋮ On some representations of the Iwahori subgroup ⋮ The pro-p-Iwahori invariants of the universal quotient representation for GL2(F) ⋮ A note on presentations of supersingular representations of \(\mathrm{GL}_2(F)\) ⋮ Iwahori-Hecke model for mod \(p\) representations of \(\mathrm{GL}(2,F)\) ⋮ Towards a modulo 𝑝 Langlands correspondence for 𝐺𝐿₂

Cites Work

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• On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields
• Weights in Serre's conjecture for Hilbert modular forms: the ramified case
• Irreducible modular representations of GL\(_ 2\) of a local field
• Serre weights for mod p Hilbert modular forms: the totally ramified case
• Reduction modulo p of cuspidal representations and weights in Serre's conjecture
• Le foncteur des invariants sous l'action du pro-p-Iwahori de GL2(F)

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