Endoscopic classification of representations of quasi-split unitary groups

By Chung Pang Mok. 2012

322 citations recorded by the source corpus.

In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77dbeaacd2f71cd4d337f4e8609de34e708ef0a0

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In Algebra and Number Theory

1. L. Clozel
2. Peter Scholze
3. Erez Lapid
4. J. Thorne
5. Zhengyu Mao
6. Lue Pan
7. T. Gee
8. W. Gan

In Discrete Mathematics and Combinatorics

1. J. Thorne
2. L. Clozel
3. Erez Lapid
4. Zhengyu Mao
5. Peter Scholze
6. W. Gan
7. Richard Harris
8. Atsushi Ichino

In Mathematical Physics

1. J. Thorne
2. Peter Scholze
3. L. Clozel
4. Erez Lapid
5. Zhengyu Mao
6. T. Gee
7. W. Gan
8. Ruochuan Liu

Citations in the corpus

• WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT $L$ -FUNCTIONS (2013, unknown): “Hence, the Asai L-functions L(s,Π, As(−1)) and L(s,Π′, As(−1)) have a pole at s = 1, by [25] or [39] Cor.”
• A conjecture on Whittaker-Fourier coefficients of cusp forms (2013, methodology): “(In all other cases we automatically have ωπi ∣∣ A∗ ≡ 1 for all i.) In all algebraic cases except SO(2n) the set ΠG(ResE/F GLm) corresponds exactly to Ψ t(G) and if φ is the corresponding parameter then Sφ ≃ (Z/2Z) k−1 (see [Art11] and [Mok12]).”
• Level-raising and symmetric power functoriality, III (2017, methodology): “Mok’s results, specifically [Mok15, Theorem 2.5.2] now applied to base change to G(E) rather than descent, imply the existence of a stable base change π of σ - a RACSD representation of G(AE) - with local components in the correct Lpackets at all finite primes; at infinite primes π is cohomological ”
• On torsion in the cohomology of locally symmetric varieties (2013, background): “Mok, [48], in the unitary case))(3), one sees that there are Galois representations for all Hecke eigenvalues appearing in H̃ i c,Kp in this case.”