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We study the weight part of Serre’s conjecture for genericn-dimensional modpGalois representations. We first generalize Herzig’s conjecture to the case where the field is ramified atpand prove the weight elimination direction of the conjecture. We then introduce a new class of weights associated ton-dimensional local modprepresentations which we callextremal weights. Using a “Levi reduction” property of certain potentially crystalline Galois deformation spaces, we prove the modularity of these weights. As a consequence, we deduce the weight part of Serre’s conjecture for unit groups of some division algebras in generic situations.
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This content will become publicly available on July 31, 2026
On wavefront sets of global Arthur packets of classical groups: Upper bound
We prove a conjecture of the first named author (2014) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of all classical groups over any number field. This conjecture generalizes the global version of the local temperedL-packet conjecture of Shahidi (1990). Under certain assumption, we also compute the wavefront sets of the unramified unitary dual for split classical groups.
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- Award ID(s):
- 1848058
- PAR ID:
- 10632551
- Publisher / Repository:
- EMS Press
- Date Published:
- Journal Name:
- Journal of the European Mathematical Society
- Volume:
- 27
- Issue:
- 9
- ISSN:
- 1435-9855
- Page Range / eLocation ID:
- 3841 to 3888
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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