On certain elements in the Bernstein center of 𝐆𝐋₂

Varma, Sandeep

doi:10.1090/s1088-4165-2013-00427-2

Represent. Theory

2013

DOI: 10.1090/s1088-4165-2013-00427-2

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On certain elements in the Bernstein center of 𝐆𝐋₂

Sandeep Varma

Abstract: Abstract. Let F be a nonarchimedean local field of residue characteristic p, and let r be an odd natural number less than p. Using the work of Moy and Tadić, we find an element z of the Bernstein center of G = GL 2 (F ) that acts on any representation π of G by the scalar z(π) = tr Frob; (Sym r •ϕ π )

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The stable Bernstein center and test functions for Shimura varieties

Haines

2014

Automorphic Forms and Galois Representations

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We elaborate the theory of the stable Bernstein center of a p-adic group G, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This conjecture provides a framework by which one might pursue the Langlands-Kottwitz method in a very general situation: not necessarily PEL Shimura varieties with arbitrary level structure at p. We give a concrete reinterpretation of the test function conjecture in the context of parahoric level structure. We also use the stable Bernstein center to formulate some of the transfer conjectures (the "fundamental lemmas") that would be needed if one attempts to use the test function conjecture to express the local Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions.

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The stable Bernstein center and test functions for Shimura varieties

Haines

2014

Automorphic Forms and Galois Representations

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show abstract

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On certain elements in the Bernstein center of 𝐆𝐋₂

Cited by 1 publication

References 9 publications

The stable Bernstein center and test functions for Shimura varieties

The stable Bernstein center and test functions for Shimura varieties

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