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SUMMARY:Joe Rabinoff (Duke U.)
DTSTART:20230127T140000Z
DTEND:20230127T150000Z
DTSTAMP:20260423T021050Z
UID:LAGARTOS/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGARTOS/53/
 ">Weakly smooth forms and Dolbeault cohomology of curves</a>\nby Joe Rabin
 off (Duke U.) as part of (LAGARTOS) Latin American Real and Tropical Geome
 try Seminar\n\n\nAbstract\nGubler and I work out a theory of weakly smooth
  forms on non-Archimedean analytic spaces closely following the constructi
 on of Chambert-Loir and Ducros\, but in which harmonic functions are force
 d to be smooth.  We call such forms "weakly smooth".  We compute the Dolbe
 ault cohomology groups of rig-smooth\, compact non-Archimedean curves with
  respect to this theory\, and show that they have the expected dimensions 
 and satisfy Poincaré duality.  We carry out this computation by giving an
  alternative characterization of weakly smooth forms on curves as pullback
 s of certain "smooth forms" on a skeleton of the curve.  This yields an is
 omorphism between the Dolbeault cohomology of the skeleton\, which can be 
 computed using standard combinatorial methods\, and the Dolbeault cohomolo
 gy of the curve.\n\nThis work is joint with Walter Gubler.\n
LOCATION:https://researchseminars.org/talk/LAGARTOS/53/
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