Journal ArticleDuke Mathematical Journal · January 1, 2023
We give a modification of Yu’s construction of supercuspidal representations of a connected reductive group G over a non-Archimedean local field F . This modification restores the validity of certain key intertwining property claims made by Yu, which were ...
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Journal ArticleJournal of Algebra · January 1, 2023
We show that a mod-ℓ-representation of a p-adic group arising from the analogue of Yu's construction is supercuspidal if and only if it arises from a supercuspidal representation of a finite reductive group. This has been previously shown by Henniart and V ...
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Journal ArticleMichigan Mathematical Journal · August 1, 2022
Let F be a nonarchimedean local field of residual characteristic p = 2. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex supercuspidal repr ...
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Journal ArticleCompositio Mathematica · December 3, 2021
Let Formula Presented be a non-archimedean local field of residual characteristic Formula Presented. Let Formula Presented be a (connected) reductive group over Formula Presented that splits over a tamely ramified field extension of Formula Presented. We r ...
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Journal ArticleInternational Mathematics Research Notices · October 1, 2021
Let G be a reductive group over a non-archimedean local field k. We provide necessary conditions and sufficient conditions for all tori of G to split over a tamely ramified extension of k. We then show the existence of good semisimple elements in every Moy ...
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Journal ArticleAnnals of Mathematics · January 1, 2021
Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we show that every ...
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Journal ArticleJournal of the European Mathematical Society · January 1, 2021
Let K be a maximal unramified extension of a non-archimedean local field with arbitrary residual characteristic p. Let G be a reductive group over K which splits over a tamely ramified extension of K. We show that the associated Moy-Prasad filtration repre ...
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Journal ArticleCambridge Journal of Mathematics · January 1, 2021
Congruences between automorphic forms have been an essential tool in number theory since Ramanujan’s discovery of congruences for the τ-function, for instance in Iwasawa theory and the Langlands program. Over time, several approaches to congruences have be ...
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Journal ArticleJournal of the London Mathematical Society · April 1, 2018
Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks out a G(F) -conju ...
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Journal ArticleDocumenta Mathematica · January 1, 2018
In the 1970's, Serre exploited congruences between qexpansion coefficients of Eisenstein series to produce p-adic families of Eisenstein series and, in turn, p-adic zeta functions. Partly through integration with more recent machinery, including Katz's app ...
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Journal ArticleCompositio Mathematica · February 1, 2017
Let be a finite extension of , let be an absolutely simple split reductive group over, and let be a maximal unramified extension of . To each point in the Bruhat-Tits building of , Moy and Prasad have attached a filtration of by bounded subgroups. In this ...
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Chapter · January 1, 2016
We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms on the Igusa tower says that if the coefficients of (sufficiently many of) th ...
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