Title <> Rigid character groups, Lubin-Tate theory, and (ϕ, Γ)--modules / Laurent Berger, Peter Schneider, Bingyong Xie

Published Providence, RI : American Mathematical Society, [2020]

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Description 1 online resource (v, 79 pages) Series Memoirs of the American Mathematical Society ; number 1275 Memoirs of the American Mathematical Society ; no. 1275. Contents Introduction Chapter 1. Lubin-Tate theory and the character variety Chapter 2. The boundary of $\mathfrak X$ and $(\varphi _L,\Gamma _L)$-modules Chapter 3. Construction of $(\varphi _L,\Gamma _L)$-modules Summary 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_{p̂\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 Notes "January 2020, volume 263, number 1275 (fifth of 7 numbers)" Bibliography Includes bibliographical references Subject Class field theory. 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]. Form Electronic book Author Schneider, P. (Peter), 1953- author. Xie, Bingyong, author ISBN 9781470456580 1470456583

Other Titles Rigid character groups, Lubin-Tate theory, and (phi, Gamma)--modules

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