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Let $$F$$ be a non-archimedean local field of residual characteristic $$p \neq 2$$ . Let $$G$$ be a (connected) reductive group over $$F$$ that splits over a tamely ramified field extension of $$F$$ . We revisit Yu's construction of smooth complex representations of $G(F)$ from a slightly different perspective and provide a proof that the resulting representations are supercuspidal. We also provide a counterexample to Proposition 14.1 and Theorem 14.2 in Yu [ Construction of tame supercuspidal representations , J. Amer. Math. Soc. 14 (2001), 579–622], whose proofs relied on a typo in a reference.
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Local types of (Γ,G)$(\Gamma ,G)$‐bundles and parahoric group schemes
Abstract Let be a simple algebraic group over an algebraically closed field . Let be a finite group acting on . We classify and compute the local types of ‐bundles on a smooth projective ‐curve in terms of the first nonabelian group cohomology of the stabilizer groups at the tamely ramified points with coefficients in . When , we prove that any generically simply connected parahoric Bruhat–Tits group scheme can arise from a ‐bundle. We also prove a local version of this theorem, that is, parahoric group schemes over the formal disc arise from constant group schemes via tamely ramified coverings.
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- Award ID(s):
- 2001365
- PAR ID:
- 10442238
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Proceedings of the London Mathematical Society
- Volume:
- 127
- Issue:
- 2
- ISSN:
- 0024-6115
- Page Range / eLocation ID:
- p. 261-294
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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