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Park, Chol
Research Interests
  • Galois representations,
  • Algebraic automorphic forms,
  • Integral p-adic Hodge theory,
  • Automorphic representations.

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On mod p local-global compatibility for GL_n(Q_p) in the ordinary case

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Title
On mod p local-global compatibility for GL_n(Q_p) in the ordinary case
Author
Park, CholQian, Zicheng
Issue Date
2022-05
Publisher
Société mathématique de France
Citation
LES MÉMOIRES DE LA SOCIÉTÉ MATHÉMATIQUE DE FRANCE, v.173, pp.vi+150
Abstract
Let p be a prime number, n>2 an integer, and F a CM field in which p splits completely. Assume that a continuous automorphic Galois representation r¯¯:Gal(Q¯¯¯¯/F)→GLn(F¯¯¯¯p) is upper-triangular and satisfies certain genericity conditions at a place w above~p, and that every subquotient of r¯¯|Gal(Q¯¯¯¯¯p/Fw) of dimension >2 is Fontaine-Laffaille generic. In this paper, we show that the isomorphism class of r¯¯|Gal(Q¯¯¯¯¯p/Fw) is determined by GLn(Fw)-action on a space of mod p algebraic automorphic forms cut out by the maximal ideal of a Hecke algebra associated to r¯¯. In particular, we show that the wildly ramified part of r¯¯|Gal(Q¯¯¯¯¯p/Fw) is determined by the action of Jacobi sum operators (seen as elements of Fp[GLn(Fp)]) on this space.
URI
https://scholarworks.unist.ac.kr/handle/201301/55892
URL
https://smf.emath.fr/publications/sur-la-compatibilite-local-global-modulo-p-pour-mathrmglnmathbbqp-dans-le-cas
DOI
10.24033/msmf.481
ISSN
0249-633X
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