2017/12/11 by Park, Chol, Qian, Zicheng
#11F33 #11F80 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1712.03799
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)\rightarrowGLn(Fp) is upper-triangular and satisfies certain genericity conditions at a place w above p, and that every subquotient of r|_Gal(Qp/Fw) of dimension >2 is Fontaine--Laffaille generic. In this paper, we show that the isomorphism class of r|_Gal(Qp/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, assuming a weight elimination result which is a theorem of Bao V. Le Hung in his forthcoming paper~\citeLeH. In particular, we show that the wildly ramified part of r|_Gal(Qp/Fw) is determined by the action of Jacobi sum operators (seen as elements of Fp[GLn(Fp)]) on this space.