Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 / / Laurent Clozel, James Arthur

• Autore: Arthur James
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1989
• Descrizione fisica: 1 online resource (248 pages) : illustrations
• Disciplina: 512/.2
• Soggetto topico: Representations of groups; Trace formulas; Automorphic forms
• Soggetto non controllato: 0E; Addition; Admissible representation; Algebraic group; Algebraic number field; Approximation; Archimedean property; Automorphic form; Automorphism; Base change; Big O notation; Binomial coefficient; Canonical map; Cartan subalgebra; Cartan subgroup; Central simple algebra; Characteristic polynomial; Closure (mathematics); Combination; Computation; Conjecture; Conjugacy class; Connected component (graph theory); Continuous function; Contradiction; Corollary; Counting; Coxeter element; Cusp form; Cyclic permutation; Dense set; Density theorem; Determinant; Diagram (category theory); Discrete series representation; Discrete spectrum; Division algebra; Eigenvalues and eigenvectors; Eisenstein series; Exact sequence; Existential quantification; Field extension; Finite group; Finite set; Fourier transform; Functor; Fundamental lemma (Langlands program); Galois extension; Galois group; Global field; Grothendieck group; Group representation; Haar measure; Harmonic analysis; Hecke algebra; Hilbert's Theorem 90; Identity component; Induced representation; Infinite product; Infinitesimal character; Invariant measure; Irreducibility (mathematics); Irreducible representation; L-function; Langlands classification; Laurent series; Lie algebra; Lie group; Linear algebraic group; Local field; Mathematical induction; Maximal compact subgroup; Multiplicative group; Nilpotent group; Orbital integral; P-adic number; Paley–Wiener theorem; Parameter; Parametrization; Permutation; Poisson summation formula; Real number; Reciprocal lattice; Reductive group; Root of unity; Scientific notation; Semidirect product; Special case; Spherical harmonics; Subgroup; Subset; Summation; Support (mathematics); Tensor product; Theorem; Trace formula; Unitary representation; Weil group; Weyl group; Zero of a function
• Classificazione: SK 240
• Persona (resp. second.): ClozelLaurent
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Bibliography.
• Nota di contenuto: Frontmatter -- Contents -- Introduction -- Chapter 1. Local Results -- Chapter 2. The Global Comparison -- Chapter 3. Base Change -- Bibliography
• Sommario/riassunto: A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.
• Titolo autorizzato: Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120
• ISBN: 1-4008-8240-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154743703321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 120.