On non-abelian Lubin-Tate theory and analytic cohomology
نویسندگان
چکیده
منابع مشابه
Survey on Non-abelian Lubin-tate Theory
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 develop...
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We give a purely local proof, in the depth 0 case, of the result by HarrisTaylor which asserts that the local Langlands correspondence for GLn is realized in the vanishing cycle cohomology of the deformation spaces of one-dimensional formal modules of height n. Our proof is given by establishing the direct geometric link with the Deligne-Lusztig theory for GLn(Fq).
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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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Motivation: We seek to understand the stable homotopy category by understanding the structure of the moduli stack of formal groups. Over algebraically closed fields, this is straightforward. If char(k) = 0, every formal group law is isomorphic to the additive one and we’ve described the group of automorphisms (coordinates changes) before. If char(k) = p > 0 every formal group law is classified ...
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We reprove Lazard’s result that every commutative n-bud is extendible to an n+ 1 bud, from an obstruction theoretic point of view. We locate the obstruction to extending an arbitrary n-bud in a certain cohomology group, and classify isomorphism classes of n-bud extensions for low degrees. 1 Lubin-Tate cohomology Definition 1. Let R be a commutative, unital ring and F a formal group law on R (as...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13716