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Niveau: Supérieur, Doctorat, Bac+8

Conditional base change for unitary groups Michael Harris ? Jean-Pierre Labesse ?? Introduction It has been known for many years that the stabilization of the Arthur-Selberg trace formula would, or perhaps we should write “will,” have important consequences for the Langlands functoriality program as well as for the study of the Galois representations on the -adic cohomology of Shimura varieties. At present, full stabilization is still only known for SL(2) and U(3) and their inner forms [LL,R]. The automorphic and arithmetic consequences of stabilization for U(3) form the subject of the influential volume [LR]. Under somewhat restrictive hypotheses, one can sometimes derive the expected corollaries of the stable trace formula. Examples of such “pseudo-stabilization” include Kottwitz' analysis in [K2] of the zeta functions of certain “simple” Shimura varieties attached to twisted forms of unitary groups over totally real fields, and the proof in [L1] of stable cyclic base change of automorphic representations which are locally Steinberg at at least two places. These conditional results have been used successfully to provide non-trivial examples of compatible systems of -adic representations attached to certain classes of automorphic representations of GL(n) [C3], and of non-trivial classes of cohomology of S-arithmetic groups [BLS, L1].

Conditional base change for unitary groups Michael Harris ? Jean-Pierre Labesse ?? Introduction It has been known for many years that the stabilization of the Arthur-Selberg trace formula would, or perhaps we should write “will,” have important consequences for the Langlands functoriality program as well as for the study of the Galois representations on the -adic cohomology of Shimura varieties. At present, full stabilization is still only known for SL(2) and U(3) and their inner forms [LL,R]. The automorphic and arithmetic consequences of stabilization for U(3) form the subject of the influential volume [LR]. Under somewhat restrictive hypotheses, one can sometimes derive the expected corollaries of the stable trace formula. Examples of such “pseudo-stabilization” include Kottwitz' analysis in [K2] of the zeta functions of certain “simple” Shimura varieties attached to twisted forms of unitary groups over totally real fields, and the proof in [L1] of stable cyclic base change of automorphic representations which are locally Steinberg at at least two places. These conditional results have been used successfully to provide non-trivial examples of compatible systems of -adic representations attached to certain classes of automorphic representations of GL(n) [C3], and of non-trivial classes of cohomology of S-arithmetic groups [BLS, L1].

- let
- group
- hermitian forms
- now let
- tate-nakayama isomorphism
- jacquet-langlands transfer
- galois cohomology
- conditions when
- trivial examples

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Published by | mijec |

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Language | English |

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