BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Modular orbifolds and derived Galois deformation theory  - Patrick
  Allen (McGill)
DTSTART:20250617T120000Z
DTEND:20250617T130000Z
UID:TALK231661@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:An example of Serre shows that in the strong form of his modul
 arity conjecture\, one can't always ask for minimal nebentypus. Serre and 
 Carayol independently explained that this obstruction is due to nontrivial
  isotropy groups on certain modular orbifolds\, hence only occurs for the 
 primes 2 and 3 and certain Galois representations called badly dihedral.\n
 \nCuriously\, when studying the deformation theory of a mod p modular Galo
 is representation for an odd prime p\, the same badly dihedral representat
 ions for p = 3 arise: it is exactly for these that the minimal deformation
  ring does not appear to be a flat local complete intersections over the r
 ing of Witt vectors.\n\nWe explain this link via a derived version of a mi
 nimal R = T theorem. As a corollary\, we can characterize when these badly
  dihedral representations admit lifts with minimal weight\, level\, and ne
 bentypus. This is joint work in progress with Preston Wake.\n
LOCATION:MR12
END:VEVENT
END:VCALENDAR