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SUMMARY:Modularity of certain trianguline Galois representations   - James
  Kiln (Queen Mary)
DTSTART:20250527T133000Z
DTEND:20250527T143000Z
UID:TALK230914@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:An unpublished result of Emerton states that every trianguline
  representation of the absolute Galois group of Q\, satisfying certain con
 ditions\, arises as a twist of the Galois representation attached to an ov
 erconvergent p-adic cuspidal eigenform of finite slope. I will outline a n
 ew approach to prove this result by patching trianguline varieties and eig
 envarieties for modular forms on GL2 to establish an “R=T” theorem in 
 the setting of rigid analytic spaces. There are several nice consequences 
 to such a theorem\, including a new approach to deduce the classicality of
  overconvergent eigenforms of small slope\, as well as applications to the
  Fontaine-Mazur conjecture.
LOCATION:MR13
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