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SUMMARY:Comparing residually reducible semisimple Galois representations [
 MPIM]
DTSTART:20250814T150000Z
DTEND:20250814T153000Z
DTSTAMP:20260420T161800Z
UID:indico-event-591@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ignasi Sánchez Rodríguez\n\nNumber theory lunch se
 minar\nLet n \\geq 2 and p be a prime. Let K be a number field andconsider
  two Galois representations \\rho_1\, \\rho_2 : \\Gal(\\Kbar / K) \\to\\GL
 _n(\\Q_p) having residual image a p-group. Is there a list T of primes ofK
  such that comparing traces of Frobenius at those primes is enough toensur
 e that the semisimplification of both \\rho_1 and \\rho_2 are isomorphic? 
 Is the list T finite? Can it be computed? How small (in norm) can theprime
 s in T be?\nLoïc Grenié gave answers to these questions in his work in 2
 007.  In thistalk we present a fully automatic implementation of Grenié'
 s work thatreturns the minimal list T. Moreover\, we use the method to pro
 ve thefollowing result: Let K=\\Q(\\sqrt{-3}) and let \\rho_1\, \\rho_2 : 
 G_K \\to\\GL_2(\\Z_3) be continuous representations unramified outside 3 h
 aving thesame determinant. Then \\rho_1 and \\rho_2 have isomorphicsemisim
 plifications if and only if \\rho_1(\\Frob_t) and \\rho_2(\\Frob_t) haveth
 e same trace for every t in K above the primes  {2\,7\,19\,73}.\n \n\nht
 tps://math-events.uni-bonn.de/event/591/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/591/
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