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SUMMARY:Reinier Sorgdrager (Université Paris-Saclay)
DTSTART:20260729T070000Z
DTEND:20260729T083000Z
DTSTAMP:20260805T015924Z
UID:HCMCAlg/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HCMCAlg/4/">
 Gelfand-Kirillov bound for GL_2</a>\nby Reinier Sorgdrager (Université Pa
 ris-Saclay) as part of KIAS HCMC Algebra Seminar\n\n\nAbstract\nLet G be a
  p-adic Lie group. In this talk I will introduce the Gelfand-Kirillov dime
 nsion of p-adic representations of G\, which is a non-commutative generali
 zation of the Krull dimension in this setting. For this\, one uses Schneid
 er-Teitelbaum's duality theory which allows one to think of p-adic Banach 
 representations of G as (duals of) modules over a completed group ring of 
 G.\nThe ``Miracle Flatness'' observation Gee-Newton shows how knowledge of
  this dimension can have strong structural consequences\, with potential a
 pplications to completed cohomology and patching. I will discuss the examp
 le of such an application found in the work of Breuil-Herzig-Hu-Morra-Schr
 aen: as a consequence of their GK-dim computation they deduce the non-vani
 shing of the candidates via patching for the p-adic Langlands corresponden
 ce for GL_2 of an unramified p-adic field.\nI will then discuss the follow
 ing result (arXiv:2602.08856): let p>2 and K be a p-adic field\; an admiss
 ible p-adic Banach representation of GL_2K whose locally analytic vectors 
 admit an infinitesimal character has GK-dimension at most [K:Q_p]. This bo
 und is optimal and improves the previous bound <2[K:Q_p] of Dospinescu-Pa
 škūnas-Schraen. \nIn my thesis I have generalized this result to familie
 s of p-adic Banach representation with an infinitesimal character in famil
 ies (in the sense of Dospinescu-Paškūnas-Schraen) and I will explain how
  this leads to a generalization of the GK-dim computation and non-vanishin
 g of candidates result of Breuil-Herzig-Hu-Morra-Schraen to GL_2K where K 
 now can have arbitrary ramification.\n
LOCATION:https://researchseminars.org/talk/HCMCAlg/4/
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