Rigid character groups, Lubin-Tate theory, and (phi,Gamma)-Modules. Memoirs of the American Mathematical Society; volume 263, number 1275 (fifth of 7 numbers).

Berger, Laurent; Schneider, Peter; Xie, Bingyong

ISBN 10: 1470440733 / ISBN 13: 9781470440732

Editore: Providence, American Mathematical Society, 2020

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Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00868 9781470440732 Sprache: Englisch Gewicht in Gramm: 150.

Codice articolo 2484707

Dati bibliografici

• Titolo: Rigid character groups, Lubin-Tate theory, and (phi,Gamma)-Modules. Memoirs of the American Mathematical Society; volume 263, number 1275 (fifth of 7 numbers).
• Editore: Providence, American Mathematical Society
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 1470440733
• ISBN 13: 9781470440732
• Rilegatura: Softcover
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

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 carried out, to some extent, by working over the $p$-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(\varphi ,\Gamma )$-modules in a different fashion. Instead of the $p$-adic open unit disk, the authors work over a character variety that parameterizes the locally $L$-analytic characters on $o_L$. They study $(\varphi ,\Gamma )$-modules in this setting and relate some of them to what was known previously.