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SUMMARY:Gabriel Dorfsman-Hopkins (UC Berkeley)
DTSTART:20211118T220000Z
DTEND:20211118T230000Z
DTSTAMP:20260423T022806Z
UID:UCSD_NTS/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/47/
 ">Untilting Line Bundles on Perfectoid Spaces</a>\nby Gabriel Dorfsman-Hop
 kins (UC Berkeley) as part of UCSD number theory seminar\n\nLecture held i
 n APM 7321 and online.\n\nAbstract\nLet $X$ be a perfectoid space with til
 t $X^\\flat$.  We build a natural map $\\theta:\\Pic X^\\flat\\to\\lim\\Pi
 c X$ where the (inverse) limit is taken over the $p$-power map\, and show 
 that $\\theta$ is an isomorphism if $R = \\Gamma(X\,\\sO_X)$ is a perfecto
 id ring.  As a consequence we obtain a characterization of when the Picard
  groups of $X$ and $X^\\flat$ agree in terms of the $p$-divisibility of $\
 \Pic X$.  The main technical ingredient is the vanishing of higher derived
  limits of the unit group $R^*$\, whence the main result follows from the 
 Grothendieck spectral sequence.\n\npre-talk at 1:20pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/47/
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