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Jessica Fintzen

Professor of Mathematics
Mathematics

Selected Publications


A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY

Journal Article Duke 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 ... Full text Cite

Supercuspidal representations in non-defining characteristics

Journal Article Journal 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 ... Full text Cite

Tame Cuspidal Representations in Non-Defining Characteristics

Journal Article Michigan 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 ... Full text Cite

On the construction of tame supercuspidal representations

Journal Article Compositio 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 ... Full text Cite

Tame Tori in p-Adic Groups and Good Semisimple Elements

Journal Article International 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 ... Full text Cite

Types for tame p-adic groups

Journal Article Annals 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 ... Full text Cite

On the Moy-Prasad filtration

Journal Article Journal 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 ... Full text Cite

Congruences of algebraic automorphic forms and supercuspidal representations

Journal Article Cambridge 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 ... Full text Cite

On Kostant sections and topological nilpotence

Journal Article Journal 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 ... Full text Cite

Differential operators and families of automorphic forms on unitary groups of arbitrary signature

Journal Article Documenta 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 ... Cite

Stable vectors in Moy-Prasad filtrations

Journal Article Compositio 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 ... Full text Cite

p-Adic q-Expansion Principles on Unitary Shimura Varieties

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 ... Full text Cite

Reflection subgroups of odd-angled Coxeter groups

Journal Article Journal of Combinatorial Theory. Series A · January 1, 2014 We give a criterion for a finitely generated odd-angled Coxeter group to have a proper finite index subgroup generated by reflections. The answer is given in terms of the least prime divisors of the exponents of the Coxeter relations. © 2014 Elsevier Inc. ... Full text Cite

Cyclotomic polynomial coefficients a(n,k) with n and k in prescribed residue classes

Journal Article Journal of Number Theory · October 1, 2011 Let a(n,k) be the kth coefficient of the nth cyclotomic polynomial. Ji, Li and Moree (2009) [2] showed that {a(n,k)|n≡0modd, n≥1,k≥0}=Z{double-struck}. In this paper we will determine {a(n,k)|n≡amodd,k≡bmodf,n≥1,k≥0}. © 2011 Elsevier Inc. ... Full text Cite