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SUMMARY:Relative GAGA theorem and geometricity of analytic mapping stacks
DTSTART:20260414T120000Z
DTEND:20260414T130000Z
DTSTAMP:20260412T085800Z
UID:indico-event-15873@indico.math.cnrs.fr
DESCRIPTION:Speakers: Qixiang Wang (Orsay)\n\nThe representability of the 
 Picard stack of a proper rigid space is a long-standing open problem in ri
 gid analytic geometry. Classical relative GAGA theorems give an affirmativ
 e answer in the algebrizable case\, but this approach does not extend to m
 ore flexible settings in modern p-adic geometry\, such as v-stacks\, essen
 tially because existing relative GAGA results are only established for noe
 therian adic spaces. Using the Clausen–Scholze formalism of analytic geo
 metry\, we show how to overcome this obstruction in a conceptual way. Alon
 g the way\, we in fact obtain a general representability result for analyt
 ic mapping stacks in the context of Gelfand stacks. In particular\, for a 
 proper algebraic source and a suitable target stack\, the analytification 
 of the algebraic mapping stack coincides with the intrinsic analytic mappi
 ng stack\, providing a new approach to representability results for analyt
 ic moduli stacks in p-adic geometry.\n\nhttps://indico.math.cnrs.fr/event/
 15873/
LOCATION:IMT 1R2 207 (Salle Pellos)
URL:https://indico.math.cnrs.fr/event/15873/
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