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SUMMARY:Intersections of the irreducible components of the Emerton-Gee sta
 ck for GL2 - Kalyani Kansal (Institute for Advanced Study)
DTSTART:20231024T133000Z
DTEND:20231024T143000Z
UID:TALK206740@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Let p be a fixed odd prime\, and let K be a finite extension o
 f Qp with ring of integers O_K. The Emerton-Gee stack for GL2 is a stack o
 f (phi\, Gamma)-modules and can be interpreted as a moduli stack of repres
 entations of the absolute Galois group of K with p-adic coefficients. The 
 irreducible components of the reduced part of the stack\, denoted X\, are 
 labelled in a natural way by Serre weights\, which are the irreducible mod
  p representations of GL2(O_K).\n\nMotivated by the conjectural categorica
 l p-adic Langlands programme\, we find representation-theoretic criteria f
 or codimension one intersections of the irreducible components of X. We sh
 ow that a non-trivial extension of a pair of non-isomorphic Serre weights 
 implies a codimension one intersection of the corresponding irreducible co
 mponents. The converse of this statement is also true when the Serre weigh
 ts are chosen to be sufficiently generic. Furthermore\, we show that the n
 umber of top-dimensional components in a codimension one intersection is r
 elated to the nature of the extension group of corresponding Serre weights
 .\n\n\n
LOCATION:https://cam-ac-uk.zoom.us/j/93515008077?pwd=NkZ5UGk2MTNueFhrb2c1R
 G96cFNPQT09
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