Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups

Roger Plymen; Anne-Marie Aubert

doi:10.1016/j.jnt.2021.06.003

Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups

Roger Plymen, Anne-Marie Aubert

Pure Mathematics

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Abstract

Let E/F be a finite and Galois extension of non-archimedean local fields. Let G be a connected reductive group defined over E and let M:=R _E/FG be the reductive group over F obtained by Weil restriction of scalars. We investigate depth, and the enhanced local Langlands correspondence, in the transition from G(E) to M(F). We obtain a depth-comparison formula for Weil-restricted groups.

Original language	English
Pages (from-to)	24-58
Number of pages	35
Journal	Journal of Number Theory
Volume	233
Early online date	21 Jul 2021
DOIs	https://doi.org/10.1016/j.jnt.2021.06.003
Publication status	Published - 28 Dec 2021

Keywords

Local field
Depth
Weil-restricted groups
Enhanced local Langlands correspondence

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10.1016/j.jnt.2021.06.003

1-s2.0-S0022314X21001992-mainAccepted author manuscript, 933 KB

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title = "Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups",

abstract = "Let E/F be a finite and Galois extension of non-archimedean local fields. Let G be a connected reductive group defined over E and let M:=R E/FG be the reductive group over F obtained by Weil restriction of scalars. We investigate depth, and the enhanced local Langlands correspondence, in the transition from G(E) to M(F). We obtain a depth-comparison formula for Weil-restricted groups.",

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AU - Plymen, Roger

AU - Aubert, Anne-Marie

PY - 2021/12/28

Y1 - 2021/12/28

N2 - Let E/F be a finite and Galois extension of non-archimedean local fields. Let G be a connected reductive group defined over E and let M:=R E/FG be the reductive group over F obtained by Weil restriction of scalars. We investigate depth, and the enhanced local Langlands correspondence, in the transition from G(E) to M(F). We obtain a depth-comparison formula for Weil-restricted groups.

AB - Let E/F be a finite and Galois extension of non-archimedean local fields. Let G be a connected reductive group defined over E and let M:=R E/FG be the reductive group over F obtained by Weil restriction of scalars. We investigate depth, and the enhanced local Langlands correspondence, in the transition from G(E) to M(F). We obtain a depth-comparison formula for Weil-restricted groups.

KW - Local field

KW - Depth

KW - Weil-restricted groups

KW - Enhanced local Langlands correspondence

U2 - 10.1016/j.jnt.2021.06.003

DO - 10.1016/j.jnt.2021.06.003

M3 - Article

VL - 233

SP - 24

EP - 58

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups

Abstract

Keywords

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