Automorphy and irreducibility of some l-adic representations

DOI10.1112/S0010437X14007519zbMath1322.11055arXiv1307.1640OpenAlexW2141453106MaRDI QIDQ4982974

Stefan Patrikis, Richard Taylor

Publication date: 13 April 2015

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

Full work available at URL: https://arxiv.org/abs/1307.1640

zbMATH Keywords

automorphic formspurityrigid local systemspotential automorphycompatible system of Galois representationsmotivated motives

Mathematics Subject Classification ID

Galois representations (11F80) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (16)

GLOBALLY REALIZABLE COMPONENTS OF LOCAL DEFORMATION RINGS ⋮ Hodge theory of Kloosterman connections ⋮ Purity for families of Galois representations ⋮ Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$ ⋮ Reciprocity in the Langlands program since Fermat's last theorem ⋮ On the images of Galois representations attached to low weight Siegel modular forms ⋮ Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations ⋮ Hodge properties of Airy moments ⋮ Hodge numbers of motives attached to Kloosterman and Airy moments ⋮ Unobstructedness of Galois deformation rings associated to regular algebraic conjugate self-dual cuspidal automorphic representations ⋮ Potential automorphy and change of weight ⋮ Variations on a Theorem of Tate ⋮ Independence of algebraic monodromy groups in compatible systems ⋮ Ordinary points \(\bmod\, p\) of \(\operatorname{GL}_n(\mathbb{R})\)-locally symmetric spaces ⋮ Irreducibility of automorphic Galois representations of low dimensions ⋮ Abelian surfaces over totally real fields are potentially modular

Cites Work

• The image of complex conjugation in \(l\)-adic representations associated to automorphic forms
• An \(\widehat{A_4}\) extension of \({\mathbb{Q}}\) attached to a non-selfdual automorphic form on \(GL(3)\)
• A family of Calabi-Yau varieties and potential automorphy
• Monodromy for the hypergeometric function \(_ nF_{n-1}\)
• On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne
• For an unconditional theory of motives
• Equivariant resolution of singularities in characteristic 0
• Variation of Hodge structure: The singularities of the period mapping
• Degeneration of Hodge structures
• La conjecture de Weil. I
• Hodge theory of the middle convolution
• Potential automorphy and change of weight
• Rigid local systems and motives of typeG₂. With an appendix by Michale Dettweiler and Nicholas M. Katz

This page was built for publication: Automorphy and irreducibility of some l-adic representations