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SUMMARY:Sheng-Chi Shih (Univ of Vienna)
DTSTART:20210222T190000Z
DTEND:20210222T195000Z
DTSTAMP:20260423T022803Z
UID:UCLA_NTS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/21/
 ">Geometry of the Hilbert cuspidal eigenvariety at weight one Eisenstein p
 oints</a>\nby Sheng-Chi Shih (Univ of Vienna) as part of UCLA Number Theor
 y Seminar\n\n\nAbstract\nIn this talk\, we will report on a joint work wit
 h Adel Betina and Mladen\nDimitrov about the geometry of the Hilbert cuspi
 dal eigenvarity at a\npoint $f$ coming from a weight one Eisenstein series
  irregular at a single\nprime $P$ of the totally real field $F$ above $p$.
 \n\nAssuming Leopoldt's conjecture for $F$ at $p$\, we show that the nearl
 y\nordinary cuspidal eigenvariety is étale at f over the weight space whe
 n\n$[F_P:Q_p]\\geq[F:Q]−1$\, and hence\, the ordinary eigencurve is éta
 le over the\nweight space as well. When $F_P=Q_p$ we show that the eigenva
 riety is\nsmooth at $f$\, while in all the remaining cases\, we prove that
  the\neigenvariety is never smooth at $f$.\n\nIf time permits\, we will al
 so discuss some applications in Iwasawa\nTheory and a new proof of the ran
 k 1 Gross-Stark conjecture.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/21/
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