Survey on Non-abelian Lubin-tate Theory
نویسنده
چکیده
We give a survey, for non-experts, of the non-abelian Lubin-Tate theory, a cohomological realization of the local Langlands correspondence over p-adic fields. As its proof at the moment (mostly given by the work of Harris-Taylor [HT]) requires global techniques using certain Shimura varieties, we will treat the arithmetic geometry of these Shimura varieties, including some of the recent developments.
منابع مشابه
Self-duality and parity in non-abelian Lubin–Tate theory
We give a geometric proof of a “parity-switching” phenomenon that occurs when applying the local Langlands and Jacquet–Langlands correspondence to a self-dual supercuspidal representation ofGL(n) over a nonarchimedean local field. This turns out to reflect a duality property on the self-dual part of the `-adic étale cohomology of the Lubin–Tate tower.
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We introduce method of approaching local class field theory from the perspective of Lubin-Tate formal groups. Our primarily aim is to demonstrate how to construct abelian extensions using these groups.
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We give a self-contained proof of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [4].
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Using Lubin-Tate groups, we develop a variant of Fontaine’s theory of (φ,Γ)-modules, and we use it to give a description of the Galois stable lattices inside certain crystalline representations.
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تاریخ انتشار 2007