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Rigid character groups, Lubin-Tate theory, and (ϕ, Γ)--modules /

The construction of the p-adic local Langlands correspondence for \mathrm{GL}_2(\mathbf{Q}_p) uses in an essential way Fontaine's theory of cyclotomic (\varphi ,\Gamma )-modules. Here cyclotomic means that \Gamma = \mathrm {Gal}(\mathbf{Q}_p(\mu_{p^\infty})/\mathbf{Q}_p) is the Galois group of...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Berger, Laurent, 1976- (Autor), Schneider, P. (Peter), 1953- (Autor), Xie, Bingyong (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society ; no. 1275.
Temas:
Class field theory.
Théorie du corps de classes.
Class field theory
Number theory > Algebraic number theory: local and $p$-adic fields > Class field theory; $p$-adic formal groups [See also 14L05].
Number theory > Algebraic number theory: local and $p$-adic fields > Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50].
Algebraic geometry > Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] > Rigid analytic geometry.
Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} > Lie groups {For the topology of Lie groups and homogeneous spaces, see.
Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} > Other (nonclassical) types of functional analysis [See also 47Sxx] > Functional analysis over fields othe.
Number theory > Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} > Galois representations.
Number theory > Algebraic number theory: local and $p$-adic fields > Galois theory.
Field theory and polynomials > Differential and difference algebra > $p$-adic differential equations [See also 11S80, 14G20].
Commutative algebra > Arithmetic rings and other special rings > Dedekind, Prüfer, Krull and Mori rings and their generalizations.
Commutative algebra > Topological rings and modules [See also 16W60, 16W80] > Power series rings [See also 13F25].
Acceso en línea:Texto completo
Descripción
Sumario:The construction of the p-adic local Langlands correspondence for \mathrm{GL}_2(\mathbf{Q}_p) uses in an essential way Fontaine's theory of cyclotomic (\varphi ,\Gamma )-modules. Here cyclotomic means that \Gamma = \mathrm {Gal}(\mathbf{Q}_p(\mu_{p^\infty})/\mathbf{Q}_p) is the Galois group of the cyclotomic extension of \mathbf Q_p. In order to generalize the p-adic local Langlands correspondence to \mathrm{GL}_{2}(L), where L is a finite extension of \mathbf{Q}_p, it seems necessary to have at our disposal a theory of Lubin-Tate (\varphi ,\Gamma )-modules. Such a generalization has been carr.
Notas:"January 2020, volume 263, number 1275 (fifth of 7 numbers)"
Descripción Física:1 online resource (v, 79 pages).
Bibliografía:Includes bibliographical references.
ISBN:9781470456580
1470456583

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