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UID:9077@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260505T140000
DTEND;TZID=Europe/Paris:20260505T150000
DTSTAMP:20260507T223816Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-297/
SUMMARY:Marco Artusa (CIRM-I2M): Towards a geometrisation of Deligne cohomo
 logy
DESCRIPTION:Marco Artusa: Deligne cohomology of a complex manifold Y is a h
 ybrid object: it mixes Betti cohomology with the Hodge filtration on de Rh
 am cohomology\, producing a complex of locally compact abelian groups. Des
 pite its central role in regulators and special-value conjectures\, it lac
 ks a geometric framework that treats the archimedean structure of de Rham 
 cohomology and the discrete structure of Betti cohomology at the same time
 .\n \nIn this talk\, we construct an analytic stack \\mathcal{X} (in the 
 sense of Clausen-Scholze) that serves as a universal base for such objects
 . Quasi-coherent sheaves on \\mathcal{X} combine archimedean (liquid) mod
 ules and non-archimedean (solid) modules. In particular\, Deligne cohomolo
 gy groups appear as quasi-coherent sheaves on \\mathcal{X}. \n \nIf time
  permits\, we present a strategy to associate\, to any complex analytic ma
 nifold Y\, an analytic stack Y^{Del} over \\mathcal{X}\, whose relative co
 homology should recover Deligne cohomology. This is a work in progress.
CATEGORIES:Séminaire,AGLR,Représentations des Groupes Réductifs
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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DTSTART:20260329T030000
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