A Quotient of the Lubin–tate Tower
نویسنده
چکیده
In this article we show that the quotient M∞/B(Qp) of the Lubin–Tate space at infinite level M∞ by the Borel subgroup of upper triangular matrices B(Qp) ⊂ GL2(Qp) exists as a perfectoid space. As an application we show that Scholze’s functor H i ét(PCp ,Fπ ) is concentrated in degree one whenever π is an irreducible principal series representation or a twist of the Steinberg representation of GL2(Qp). 2010 Mathematics Subject Classification: 11S37 (primary); 14G22 (secondary)
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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