Maximality of Galois actions for compatible systems

DOI10.1215/S0012-7094-95-08021-1zbMath0912.11026MaRDI QIDQ1911599

Michael J. Larsen

Publication date: 30 May 1999

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

maximality\(\ell\)-adic Galois representationsGalois actioncompatible system of representationscohomology representations

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Langlands-Weil conjectures, nonabelian class field theory (11S37) Linear algebraic groups over local fields and their integers (20G25)

Related Items (33)

Geometric monodromy -- semisimplicity and maximality ⋮ Functoriality and the inverse Galois problem. II: Groups of type \(B_n\) and \(G_2\) ⋮ INTEGRAL MONODROMY GROUPS OF KLOOSTERMAN SHEAVES ⋮ Type A images of Galois representations and maximality ⋮ Moduli of parahoric 𝒢-torsors on a compact Riemann surface ⋮ Local models of Shimura varieties and a conjecture of Kottwitz ⋮ Maximality of Galois actions for abelian and hyper-Kähler varieties ⋮ The integral monodromy of hyperelliptic and trielliptic curves ⋮ Monodromy of four‐dimensional irreducible compatible systems of Q$\mathbb {Q}$ ⋮ Computing finite Galois groups arising from automorphic forms ⋮ Roots of \(L\)-functions of characters over function fields, generic linear independence and biases ⋮ Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations ⋮ INTEGRAL AND ADELIC ASPECTS OF THE MUMFORD–TATE CONJECTURE ⋮ Remarks on the inverse Galois problem over function fields ⋮ On class numbers of division fields of abelian varieties ⋮ Potential automorphy over CM fields ⋮ Explicit bounds for split reductions of simple abelian varieties ⋮ COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP ⋮ Potential automorphy and change of weight ⋮ Monodromy for some rank two Galois representations over CM fields ⋮ Potentially 𝐺𝐿₂-type Galois representations associated to noncongruence modular forms ⋮ Embeddings of \(\text{PGL}_2(31)\) and \(\text{SL}_2(32)\) in \(E_8(\mathbb{C})\). With appendices by Michael Larsen and J. -P. Serre ⋮ Big symplectic or orthogonal monodromy modulo \(\ell\) ⋮ A family of Calabi-Yau varieties and potential automorphy ⋮ On the image of Galois \(l\)-adic representations for abelian varieties of type III ⋮ Motivic Galois representations valued in spin groups ⋮ ON THE RANK OF QUADRATIC TWISTS OF ELLIPTIC CURVES OVER FUNCTION FIELDS ⋮ On the semisimplicity of reductions and adelic openness for 𝐸-rational compatible systems over global function fields ⋮ On the universal coverings of algebraic surfaces ⋮ Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion ⋮ Semistable principal bundles. I: Characteristic zero. ⋮ Bigness in Compatible Systems ⋮ Galois groups arising from families with big orthogonal monodromy

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