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SUMMARY:Reinier Sorgdrager (Université Paris-Saclay)
DTSTART:20260729T070000Z
DTEND:20260729T083000Z
DTSTAMP:20260712T233613Z
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\nInteractive livestream
 : https://kias-re-kr.zoom.us/j/86995427727?pwd=9ZJzMvmF7AVhRZjKwQW6aXM8u7y
 ORa.1\nPassword hint: Password is the size of GL_2(F_7).\n\nAbstract\nLet 
 G be a p-adic Lie group. In this talk I will introduce the Gelfand-Kirillo
 v dimension of p-adic representations of G\, which is a non-commutative ge
 neralization of the Krull dimension in this setting. For this\, one uses S
 chneider-Teitelbaum's duality theory which allows one to think of p-adic B
 anach representations of G as (duals of) modules over a completed group ri
 ng of G.\nThe ``Miracle Flatness'' observation Gee-Newton shows how knowle
 dge of this dimension can have strong structural consequences\, with poten
 tial applications to completed cohomology and patching. I will discuss the
  example of such an application found in the work of Breuil-Herzig-Hu-Morr
 a-Schraen: as a consequence of their GK-dim computation they deduce the no
 n-vanishing of the candidates via patching for the p-adic Langlands corres
 pondence for GL_2 of an unramified p-adic field.\nI will then discuss the 
 following result (arXiv:2602.08856): let p>2 and K be a p-adic field\; an 
 admissible p-adic Banach representation of GL_2K whose locally analytic ve
 ctors admit an infinitesimal character has GK-dimension at most [K:Q_p]. T
 his bound is optimal and improves the previous bound <2[K:Q_p] of Dospines
 cu-Paškūnas-Schraen. \nIn my thesis I have generalized this result to fa
 milies of p-adic Banach representation with an infinitesimal character in 
 families (in the sense of Dospinescu-Paškūnas-Schraen) and I will explai
 n how this leads to a generalization of the GK-dim computation and non-van
 ishing of candidates result of Breuil-Herzig-Hu-Morra-Schraen to GL_2K whe
 re K now can have arbitrary ramification.\n
LOCATION:https://researchseminars.org/talk/HCMCAlg/4/
URL:https://kias-re-kr.zoom.us/j/86995427727?pwd=9ZJzMvmF7AVhRZjKwQW6aXM8u
 7yORa.1
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