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SUMMARY:Luis Dieulefait (Universitat de Barcelona)
DTSTART:20201215T123000Z
DTEND:20201215T133000Z
DTSTAMP:20260418T095410Z
UID:NTRV/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTRV/1/">Pot
 entially diagonalizable modular lifts of arbitrarily large weight</a>\nby 
 Luis Dieulefait (Universitat de Barcelona) as part of Number Theory and Re
 presentations in Valparaiso\n\n\nAbstract\nI will begin this talk by recal
 ling the notion of "potential diagonalizability"\, due to Barnet-Lamb\, Ge
 e\, Geraghty and Taylor\, and how (and why) this notion appears in Automor
 phy Lifting Theorems (in the work of the aforementioned authors).\nThen I 
 will present the main result of this talk\, which is joint work with Iván
  Blanco: existence of modular lifts of arbitrarily large weight (of a give
 n residual modular Galois representations) which are potentially diagonali
 zable. In the non-ordinary case\, the proof of this result requires a comb
 ination of local and global results for Galois deformation rings\, a local
  to global principle due to Böckle and a potential variant of the result 
 we want to prove due to Barnet-Lamb\, Gee\, Geraghty and Taylor.\nI will a
 lso explain how this result is a useful tool in the proof of some cases of
  Langlands functoriality.\n
LOCATION:https://researchseminars.org/talk/NTRV/1/
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