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SUMMARY:Infinitesimal action on completed cohomology for GL_n over a CM fi
 eld [Arithmetic Geometry and Representation Theory Research Seminar]
DTSTART:20260414T130500Z
DTEND:20260414T150500Z
DTSTAMP:20260716T204800Z
UID:indico-event-1186@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jelena Ivancic\n\nI will talk about joint work with 
 Vaughan McDonald which confirms a conjecture of Dospinescu-Paskunas-Schrae
 n (localised suitably) for reductive group GL_n/F for F a CM field contain
 ing an imaginary quadratic field where a fixed prime p splits.\n\nIn the f
 irst part of the talk\, I will recall some facts about completed cohomolog
 y of a reductive group $G$ and give a motivation (at least for me) for one
  to think there might be a relationship between:\n1.  action of the centre
  of universal algebra Z(g) of G on locally analytic vectors of completed c
 ohomology\, and\n2. Hodge--Tate--Sen weights of Galois representations att
 ached to Hecke eigenspaces\n\nThen I will introduce the relevant construct
 ions from Dospinescu-Paskunas-Schraen in some detail\, state their conject
 ure on the relationship between 1) and 2)\, and state our theorem.\n\nIn t
 he second part of the talk\, I will show the proof strategy and highlight 
 the most important ingredients.\n\nhttps://math-events.uni-bonn.de/event/1
 186/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1186/
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