BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Reinier Sorgdrager DTSTART:20261104T160000Z DTEND:20261104T170000Z DTSTAMP:20261107T050911Z UID:LNTS/205 DESCRIPTION:Title: B ound on the Gelfand-Kirillov dimension for GL_2\nby Reinier Sorgdrager as part of London number theory seminar\n\nLecture held in Imperial Colle ge London\, Huxley 139.\n\nAbstract\nThe Gelfand-Kirillov dimension of p-a dic representations of a p-adic Lie group G is a non-commutative generaliz ation of the Krull dimension for modules\, to modules over Iwasawa and dis tribution algebras of G. As observed by Gee-Newton\, knowing this dimensio n in the setting of completed/mod p cohomology or patching can lead to pro gress towards big R=T theorems.\nIn my thesis I proved that any admissible p-adic Banach representation of GL_2K (K a p-adic field) with an infinite simal character has GK-dimension at most [K:Q_p]. I have also proved a ver sion in families\, and a version for quaternion units. The family version can be applied to many Hecke eigenspaces of completed cohomology or to pat ched modules\, by Dospinescu-Paškūnas-Schraen\, Paškūnas-Quast\, and m ost recently Ivančić-McDonald\, who have shown the presence of infinites imal characters in families in several cases. For example\, the results of Breuil-Herzig-Hu-Morra-Schraen on GK-dimensions of smooth mod p represent ations of GL_2K can be generalized beyond K unramified.\nIn my talk I inte nd to focus on the general result and sketch its proof in the case of GL_2 Q_p. I will touch only briefly on applications\, many of which still need to be worked out.\n LOCATION:https://researchseminars.org/talk/LNTS/205/ END:VEVENT END:VCALENDAR