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SUMMARY:Families of Drinfeld modular forms for GL(N) - Marc-Hubert Nicole 
 (Montréal/Marseille)
DTSTART:20190604T133000Z
DTEND:20190604T143000Z
UID:TALK124708@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:Hida once described his theory of families of ordinary p-adic 
 modular eigenforms as obtained from cutting «the clear surface out of the
  pitch-dark well too deep to see through » of the space of all elliptic m
 odular forms.\nIn this talk\, we shall peer into the well of Drinfeld modu
 lar forms instead of classical modular forms.\nMore precisely\, we shall e
 xplain how to construct families of finite slope Drinfeld modular forms ov
 er Drinfeld modular varieties of any dimension.\nIn the ordinary case (the
  « clear surface »)\, we show that the weight may vary p-adically in fam
 ilies of Drinfeld modular forms (a direct analogue of Hida’s Vertical Co
 ntrol Theorem). In the deeper & murkier waters of positive slope\, the sit
 uation is more subtle: the weight may indeed vary continuously\, but not a
 nalytically\, thereby contrasting markedly with Coleman’s well-known p-a
 dic theory. (Joint work with G. Rosso.)
LOCATION:MR13
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